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146 relations: Abraham Fraenkel, Akihiro Kanamori, Argument of a function, Association for Symbolic Logic, Atomic formula, Axiom, Axiom of choice, Axiom of extensionality, Axiom of global choice, Axiom of infinity, Axiom of limitation of size, Axiom of pairing, Axiom of power set, Axiom of regularity, Axiom of union, Axiom schema, Axiom schema of replacement, Axiom schema of specification, Axiomatic system, Binary relation, Boolean algebra, Cardinality, Cartesian product, Category (mathematics), Category of sets, Category of small categories, Category theory, Charles Parsons (philosopher), Choice function, Class (set theory), Complement (set theory), Computer program, Conglomerate (set theory), Conservative extension, Consistency, Constructible universe, Continuum hypothesis, Contradiction, Crelle's Journal, Cumulative hierarchy, Cyclic permutation, Dmitry Mirimanoff, Domain of discourse, Element (mathematics), Elliott Mendelson, Empty set, Equality (mathematics), Equiconsistency, Ernst Schröder, Ernst Zermelo, ..., Existential quantification, Finitary relation, First-order logic, Forcing (mathematics), Formal system, Foundations of mathematics, Free variables and bound variables, Function (mathematics), Function application, Function composition, Fundamenta Mathematicae, Gödel's incompleteness theorems, Georg Cantor, Hao Wang (academic), Heine–Borel theorem, Hereditarily countable set, Identity function, Inaccessible cardinal, Independence (mathematical logic), Institute for Advanced Study, Intersection (set theory), John von Neumann, Journal of Symbolic Logic, Kenneth Kunen, Kurt Gödel, List of logic symbols, Logical biconditional, Logical conjunction, Logical equivalence, Material conditional, Mathematical analysis, Mathematical induction, Mathematical logic, Mathematische Zeitschrift, Metatheorem, Metatheory, Model theory, Morphism, Morse–Kelley set theory, Natural number, Nicolas Bourbaki, Ontology, Operation (mathematics), Order isomorphism, Order theory, Ordered pair, Ordinal number, Pascal (programming language), Paul Bernays, Paul Cohen, Permutation, Power set, Primitive notion, Principia Mathematica, Principle of explosion, Proceedings of the National Academy of Sciences of the United States of America, Proof by contradiction, Propositional function, Pseudocode, Pure mathematics, Quantifier (logic), Quasi-category, Recursion, Recursion (computer science), Recursive definition, Restriction (mathematics), Richard Dedekind, Richard Laver, Richard Montague, Robert M. Solovay, Ronald Jensen, Samuel Buss, Saul Kripke, Set (mathematics), Set theory, Set Theory: An Introduction to Independence Proofs, Structural induction, Structure (mathematical logic), Successor cardinal, Surjective function, Switch statement, Term (logic), The Mathematical Intelligencer, Thoralf Skolem, Transfinite number, Transitive set, Tuple, Union (set theory), Von Neumann universe, Well-formed formula, Well-founded relation, Well-order, Well-ordering theorem, William Bigelow Easton, Zermelo set theory, Zermelo–Fraenkel set theory. Expand index (96 more) »
Abraham Fraenkel
Abraham Halevi (Adolf) Fraenkel (אברהם הלוי (אדולף) פרנקל; February 17, 1891 – October 15, 1965), known as Abraham Fraenkel, was a German-born Israeli mathematician.
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Akihiro Kanamori
is a Japanese-born American mathematician.
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Argument of a function
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
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Association for Symbolic Logic
The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic.
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Atomic formula
In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Axiom of extensionality
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory.
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Axiom of global choice
In mathematics, specifically in class theories, the axiom of global choice is a stronger variant of the axiom of choice that applies to proper classes of sets as well as sets of sets.
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Axiom of infinity
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory.
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Axiom of limitation of size
In set theory, the axiom of limitation of size was proposed by John von Neumann in his 1925 axiom system for sets and classes.
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Axiom of pairing
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory.
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Axiom of power set
In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.
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Axiom of regularity
In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: The axiom implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.
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Axiom of union
In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory.
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Axiom schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
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Axiom schema of replacement
In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.
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Axiom schema of specification
In many popular versions of axiomatic set theory the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema.
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Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
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Category of sets
In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.
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Category of small categories
In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Charles Parsons (philosopher)
Charles Dacre Parsons (born April 13, 1933) is an American philosopher best known for his work in the philosophy of mathematics and the study of the philosophy of Immanuel Kant.
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Choice function
A choice function (selector, selection) is a mathematical function f that is defined on some collection X of nonempty sets and assigns to each set S in that collection some element f(S) of S. In other words, f is a choice function for X if and only if it belongs to the direct product of X.
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Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
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Complement (set theory)
In set theory, the complement of a set refers to elements not in.
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Computer program
A computer program is a collection of instructions for performing a specific task that is designed to solve a specific class of problems.
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Conglomerate (set theory)
In mathematics, a conglomerate is a collection of classes, just as a class is a collection of sets.
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Conservative extension
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory.
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Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
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Constructible universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets that can be described entirely in terms of simpler sets.
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Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
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Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.
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Crelle's Journal
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
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Cumulative hierarchy
In mathematical set theory, a cumulative hierarchy is a family of sets Wα indexed by ordinals α such that.
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Cyclic permutation
In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (that is, mapping to themselves) all other elements of X. If S has k elements, the cycle is called a k-cycle.
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Dmitry Mirimanoff
Dmitry Semionovitch Mirimanoff (Дми́трий Семёнович Мирима́нов, 13 September 1861, Pereslavl-Zalessky, Russia – 5 January 1945, Geneva, Switzerland) became a doctor of mathematical sciences in 1900, in Geneva, and taught at the universities of Geneva and Lausanne.
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Domain of discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Elliott Mendelson
Elliott Mendelson (born 1931) is an American logician.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
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Equiconsistency
In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa.
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Ernst Schröder
Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic.
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Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo (27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
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Existential quantification
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
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Finitary relation
In mathematics, a finitary relation has a finite number of "places".
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results.
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Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
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Foundations of mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
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Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function application
In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Fundamenta Mathematicae
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.
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Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Hao Wang (academic)
Hao Wang (20 May 1921 – 13 May 1995) was a logician, philosopher, mathematician, and commentator on Kurt Gödel.
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Heine–Borel theorem
In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements are equivalent.
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Hereditarily countable set
In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Inaccessible cardinal
In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic.
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Independence (mathematical logic)
In mathematical logic, independence refers to the unprovability of a sentence from other sentences.
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Institute for Advanced Study
The Institute for Advanced Study (IAS) in Princeton, New Jersey, in the United States, is an independent, postdoctoral research center for theoretical research and intellectual inquiry founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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John von Neumann
John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.
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Journal of Symbolic Logic
The Journal of Symbolic Logic is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic.
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Kenneth Kunen
Herbert Kenneth Kunen (born August 2, 1943) is an emeritus professor of mathematics at the University of Wisconsin–Madison who works in set theory and its applications to various areas of mathematics, such as set-theoretic topology and measure theory.
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Kurt Gödel
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
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List of logic symbols
In logic, a set of symbols is commonly used to express logical representation.
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Logical biconditional
In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "P if and only if Q", where P is an antecedent and Q is a consequent.
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Logical conjunction
In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.
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Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.
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Material conditional
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematical induction
Mathematical induction is a mathematical proof technique.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Mathematische Zeitschrift
Mathematische Zeitschrift (German for Mathematical Journal) is a mathematical journal for pure and applied mathematics published by Springer Verlag.
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Metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage.
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Metatheory
A metatheory or meta-theory is a theory whose subject matter is some theory.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Morse–Kelley set theory
In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG).
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.
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Ontology
Ontology (introduced in 1606) is the philosophical study of the nature of being, becoming, existence, or reality, as well as the basic categories of being and their relations.
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Operation (mathematics)
In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.
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Order isomorphism
In the mathematical field of order theory an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets).
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Order theory
Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Ordinal number
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
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Pascal (programming language)
Pascal is an imperative and procedural programming language, which Niklaus Wirth designed in 1968–69 and published in 1970, as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honor of the French mathematician, philosopher and physicist Blaise Pascal. Pascal was developed on the pattern of the ALGOL 60 language. Wirth had already developed several improvements to this language as part of the ALGOL X proposals, but these were not accepted and Pascal was developed separately and released in 1970. A derivative known as Object Pascal designed for object-oriented programming was developed in 1985; this was used by Apple Computer and Borland in the late 1980s and later developed into Delphi on the Microsoft Windows platform. Extensions to the Pascal concepts led to the Pascal-like languages Modula-2 and Oberon.
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Paul Bernays
Paul Isaac Bernays (17 October 1888 – 18 September 1977) was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics.
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Paul Cohen
Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
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Primitive notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept.
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Principia Mathematica
The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
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Principle of explosion
The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ), "from falsehood, anything (follows)", or ex contradictione (sequitur) quodlibet (ECQ), "from contradiction, anything (follows)"), or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction.
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Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.
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Proof by contradiction
In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition.
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Propositional function
A propositional function in logic, is a sentence expressed in a way that would assume the value of true or false, except that within the sentence is a variable (x) that is not defined or specified, which leaves the statement undetermined.
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Pseudocode
Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.
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Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
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Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
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Quasi-category
In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category.
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Recursion
Recursion occurs when a thing is defined in terms of itself or of its type.
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Recursion (computer science)
Recursion in computer science is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem (as opposed to iteration).
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Recursive definition
A recursive definition (or inductive definition) in mathematical logic and computer science is used to define the elements in a set in terms of other elements in the set (Aczel 1978:740ff).
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Restriction (mathematics)
In mathematics, the restriction of a function f is a new function f\vert_A obtained by choosing a smaller domain A for the original function f. The notation f is also used.
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Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.
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Richard Laver
Richard Joseph Laver (October 20, 1942 – September 19, 2012) was an American mathematician, working in set theory.
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Richard Montague
Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician and philosopher.
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Robert M. Solovay
Robert Martin Solovay (born December 15, 1938) is an American mathematician specializing in set theory.
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Ronald Jensen
Ronald Björn Jensen (born April 1, 1936) is an American mathematician active in Europe, primarily known for his work in mathematical logic and set theory.
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Samuel Buss
Samuel R. (Sam) Buss is an American computer scientist and mathematician who has made major contributions to the fields of mathematical logic, complexity theory and proof complexity.
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Saul Kripke
Saul Aaron Kripke (born November 13, 1940) is an American philosopher and logician.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Set Theory: An Introduction to Independence Proofs
Set Theory: An Introduction to Independence Proofs is a textbook and reference work in set theory by Kenneth Kunen.
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Structural induction
Structural induction is a proof method that is used in mathematical logic (e.g., in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields.
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Structure (mathematical logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
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Successor cardinal
In the theory of cardinal numbers, we can define a successor operation similar to that in the ordinal numbers.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Switch statement
In computer programming languages, a switch statement is a type of selection control mechanism used to allow the value of a variable or expression to change the control flow of program execution via a multiway branch.
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Term (logic)
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.
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The Mathematical Intelligencer
The Mathematical Intelligencer is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.
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Thoralf Skolem
Thoralf Albert Skolem (23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic and set theory.
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Transfinite number
Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.
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Transitive set
In set theory, a set A is called transitive if either of the following equivalent conditions hold.
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Von Neumann universe
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well-founded sets.
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Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
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Well-founded relation
In mathematics, a binary relation, R, is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.
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Well-order
In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.
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Well-ordering theorem
In mathematics, the well-ordering theorem states that every set can be well-ordered.
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William Bigelow Easton
William Bigelow Easton is a mathematician who proved Easton's theorem about the possible values of the continuum function.
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Zermelo set theory
Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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Redirects here:
Axiom schema of Class Comprehension, Bernays-Godel set theory, Bernays-Goedel set theory, Bernays-Gödel set theory, Bernays–Gödel set theory, NBG set theory, NBG's axiom of replacement, NBG's axiom of separation, Neumann-Bernays-Godel Axiomatic Set Theory, Neumann-Bernays-Godel set theory, Neumann-Bernays-Goedel Axiomatic Set Theory, Neumann-Bernays-Goedel set theory, Neumann-Bernays-Gödel Axiomatic Set Theory, Neumann-Bernays-Gödel set theory, VNBG, Von Neumann-Bernays-Godel Set Theory, Von Neumann-Bernays-Godel axioms, Von Neumann-Bernays-Godel set theory, Von Neumann-Bernays-Goedel Set Theory, Von Neumann-Bernays-Goedel axioms, Von Neumann-Bernays-Gödel Set Theory, Von Neumann-Bernays-Gödel axioms, Von Neumann-Bernays-Gödel set theory, Von Neumann–Bernays–Godel set theory, Von Neumann–Bernays–Gödel Set Theory, Von Neumann–Bernays–Gödel axioms.
References
[1] https://en.wikipedia.org/wiki/Von_Neumann–Bernays–Gödel_set_theory
