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143 relations: Absolute geometry, Abstract algebra, Abstract state machines, Abstraction (mathematics), Agent-based model, Alessandro Padoa, Alfred Tarski, Algebra, Arithmetices principia, nova methodo exposita, Artificial life, Axiom, Axiom of pairing, Axiom schema, Belief–desire–intention software model, Benz plane, Bertrand Russell's philosophical views, Blaise Pascal, Boolean algebra, Boolean algebras canonically defined, Burrows–Abadi–Needham logic, Busy beaver, Chaitin's constant, Coherentism, Cointerpretability, Conceptual model, Construction of the real numbers, Contradiction, Cornelius Castoriadis, Craig's theorem, Creative and productive sets, Daniell integral, David Hilbert, Dedekind-infinite set, Descriptive interpretation, Drama annotation, E. H. Moore, Ernst Zermelo, Euclid, Euclidean geometry, Finitary, First principle, First-order logic, Formal language, Formal proof, Formal system, Formal theory, Formalism (philosophy), Foundations of geometry, Foundations of mathematics, Frame of reference, ..., Freedom of choice, Frege's propositional calculus, Fully probabilistic design, Functional dependency, Gaetano Fichera, Gödel's incompleteness theorems, Genetic method, Geometry, Gisbert Hasenjaeger, Giuseppe Peano, Glossary of areas of mathematics, Gottlob Frege, Greek letters used in mathematics, science, and engineering, Gunnar Kangro, Hilbert's axioms, Hilbert's sixth problem, History of geometry, History of logic, History of mathematical notation, History of mathematics, History of randomness, Identity of indiscernibles, Index of logic articles, Index of philosophy articles (A–C), Inference, Isaak Revzin, John von Neumann, Joseph Berger (sociologist), Joseph Sgro, Kolmogorov complexity, Kripke–Platek set theory with urelements, Kurt Gödel, Lambda, Large cardinal, Leon Chwistek, List of axioms, List of mathematical logic topics, Local quantum field theory, Logicism, Mathematical economics, Mathematical proof, Mathematics, Mathematics education, Measure (mathematics), Mereology, Metamathematics, Models of scientific inquiry, Named set theory, Natural number, Ordered field, Oriented matroid, Outline of logic, Paradoxes of set theory, Pedagogical grammar, Philosophy of mathematics, Point–line–plane postulate, Positivism, Primitive notion, Probability theory, Pure mathematics, Quantity calculus, Ratnatraya, Real number, Recursion, Relationship between mathematics and physics, Richard Balam, Richard von Mises, Rigour, Russell's paradox, Saccheri–Legendre theorem, Samuil Shatunovsky, Scientific modelling, Separation axiom, Set theory, Skolem's paradox, Soundness, Stevens's power law, Substitution (logic), Suslin's problem, Syntactic Structures, Synthetic geometry, Tarski's axiomatization of the reals, Tautology (logic), Theory (mathematical logic), Timeline of geometry, Timeline of mathematics, Timeline of thermodynamics, Undecidable problem, Van Hiele model, Von Neumann–Bernays–Gödel set theory, Where Mathematics Comes From, Whitehead's point-free geometry, Zermelo–Fraenkel set theory. Expand index (93 more) »
Absolute geometry
Absolute geometry is a geometry based on an axiom system for Euclidean geometry with the parallel postulate removed and none of its alternatives used in place of it.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Abstract state machines
In computer science, an abstract state machine (ASM) is a state machine operating on states that are arbitrary data structures (structure in the sense of mathematical logic, that is a nonempty set together with a number of functions (operations) and relations over the set).
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Abstraction (mathematics)
Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
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Agent-based model
An agent-based model (ABM) is a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole.
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Alessandro Padoa
Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano.
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Alfred Tarski
Alfred Tarski (January 14, 1901 – October 26, 1983), born Alfred Teitelbaum,School of Mathematics and Statistics, University of St Andrews,, School of Mathematics and Statistics, University of St Andrews.
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Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Arithmetices principia, nova methodo exposita
The 1889 treatise Arithmetices principia, nova methodo exposita (The principles of arithmetic, presented by a new method; 1889) by Giuseppe Peano is a seminal document in mathematical logic and set theory, introducing what is now the standard axiomatization of the natural numbers, and known as the Peano axioms, as well as some pervasive notations, such as the symbols for the basic set operations ∈, ⊂, ∩, ∪, and ''A''−''B''.
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Artificial life
Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry.
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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 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 schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
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Belief–desire–intention software model
The belief–desire–intention software model (usually referred to simply, but ambiguously, as BDI) is a software model developed for programming intelligent agents.
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Benz plane
In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz.
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Bertrand Russell's philosophical views
The aspects of Bertrand Russell views on philosophy cover the changing viewpoints of philosopher and mathematician Bertrand Russell (1872–1970), from his early writings in 1896 until his death in February 1970.
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Blaise Pascal
Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian.
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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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Boolean algebras canonically defined
Boolean algebra is a mathematically rich branch of abstract algebra.
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Burrows–Abadi–Needham logic
Burrows–Abadi–Needham logic (also known as the BAN logic) is a set of rules for defining and analyzing information exchange protocols.
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Busy beaver
The busy beaver game consists of designing a halting, binary-alphabet Turing machine which writes the most 1s on the tape, using only a limited set of states.
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Chaitin's constant
In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt.
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Coherentism
Coherentism is the name given to a few philosophical theories in modern epistemology.
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Cointerpretability
In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of T. The "translation" here is required to preserve the logical structure of formulas.
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Conceptual model
A conceptual model is a representation of a system, made of the composition of concepts which are used to help people know, understand, or simulate a subject the model represents.
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Construction of the real numbers
In mathematics, there are several ways of defining the real number system as an ordered field.
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Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.
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Cornelius Castoriadis
Cornelius Castoriadis (Κορνήλιος Καστοριάδης; 11 March 1922 – 26 December 1997) was a Greek-FrenchMemos 2014, p. 18: "he was...
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Craig's theorem
In mathematical logic, Craig's theorem states that any recursively enumerable set of well-formed formulas of a first-order language is (primitively) recursively axiomatizable.
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Creative and productive sets
In computability theory, productive sets and creative sets are types of sets of natural numbers that have important applications in mathematical logic.
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Daniell integral
In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced.
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David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
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Dedekind-infinite set
In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. A set is Dedekind-finite if it is not Dedekind-infinite.
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Descriptive interpretation
According to Rudolf Carnap, in logic, an interpretation is a descriptive interpretation (also called a factual interpretation) if at least one of the undefined symbols of its formal system becomes, in the interpretation, a descriptive sign (i.e., the name of single objects, or observable properties).
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Drama annotation
Drama annotation is the process of annotating the metadata of a drama.
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E. H. Moore
Eliakim Hastings Moore (January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician.
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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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Euclid
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
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Finitary
In mathematics or logic, a finitary operation is an operation of finite arity, that is an operation that takes a finite number of input values.
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First principle
A first principle is a basic, foundational, self-evident proposition or assumption that cannot be deduced from any other proposition or assumption.
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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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Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
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Formal proof
A formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference.
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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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Formal theory
Formal theory can refer to.
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Formalism (philosophy)
The term formalism describes an emphasis on form over content or meaning in the arts, literature, or philosophy.
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Foundations of geometry
Foundations of geometry is the study of geometries as axiomatic systems.
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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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Frame of reference
In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements.
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Freedom of choice
Freedom of choice describes an individual's opportunity and autonomy to perform an action selected from at least two available options, unconstrained by external parties.
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Frege's propositional calculus
In mathematical logic Frege's propositional calculus was the first axiomatization of propositional calculus.
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Fully probabilistic design
Decision making (DM) can be seen purposeful choice of action sequences.
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Functional dependency
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database.
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Gaetano Fichera
Gaetano Fichera (8 February 1922 – 1 June 1996) was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables.
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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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Genetic method
The genetic method is a method of teaching mathematics coined by Otto Toeplitz in 1927.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Gisbert Hasenjaeger
Gisbert F. R. Hasenjaeger (June 1, 1919 – September 2, 2006) was a German mathematical logician.
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Giuseppe Peano
Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.
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Glossary of areas of mathematics
This is a glossary of terms that are or have been considered areas of study in mathematics.
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Gottlob Frege
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
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Greek letters used in mathematics, science, and engineering
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
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Gunnar Kangro
Gunnar Kangro (November 21, 1913, Tartu – December 25, 1975, Tartu) was an Estonian mathematician.
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Hilbert's axioms
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry.
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Hilbert's sixth problem
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent.
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History of geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships.
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History of logic
The history of logic deals with the study of the development of the science of valid inference (logic).
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History of mathematical notation
The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness.
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History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
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History of randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate.
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Identity of indiscernibles
The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common.
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Index of logic articles
No description.
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Index of philosophy articles (A–C)
No description.
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Inference
Inferences are steps in reasoning, moving from premises to logical consequences.
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Isaak Revzin
Isaak Iosifovic Revzin (Исаак Иосифович Ревзин; 1923–1974) was a Russian linguist and semiotician associated with the Tartu–Moscow Semiotic School.
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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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Joseph Berger (sociologist)
Joseph Berger (born 1924) is an American sociologist and social psychologist best known for co-founding expectation states theory.
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Joseph Sgro
Joseph A. Sgro (born September 20, 1949, San Diego, California) is a mathematician, neurologist / neurophysiologist, and an engineering technologist / entrepreneur in the field of frame grabbers, high-speed cameras, smart cameras, image processors, and related computer vision and machine vision technologies.
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Kolmogorov complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of the shortest computer program (in a predetermined programming language) that produces the object as output.
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Kripke–Platek set theory with urelements
The Kripke–Platek set theory with urelements (KPU) is an axiom system for set theory with urelements, based on the traditional (urelement-free) Kripke–Platek set 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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Lambda
Lambda, Λ, λ (uppercase Λ, lowercase λ; λάμ(β)δα lám(b)da) is the 11th letter of the Greek alphabet.
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Large cardinal
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.
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Leon Chwistek
Leon Chwistek (Kraków, Austria-Hungary, 13 June 1884 – 20 August 1944, Barvikha near Moscow, Russia) was a Polish avant-garde painter, theoretician of modern art, literary critic, logician, philosopher and mathematician.
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List of axioms
This is a list of axioms as that term is understood in mathematics, by Wikipedia page.
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List of mathematical logic topics
This is a list of mathematical logic topics, by Wikipedia page.
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Local quantum field theory
The Haag–Kastler axiomatic framework for quantum field theory, introduced by, is an application to local quantum physics of C*-algebra theory.
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Logicism
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.
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Mathematical economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
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Mathematical proof
In mathematics, a proof is an inferential argument for a mathematical statement.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Mereology
In philosophy and mathematical logic, mereology (from the Greek μέρος meros (root: μερε- mere-, "part") and the suffix -logy "study, discussion, science") is the study of parts and the wholes they form.
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Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods.
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Models of scientific inquiry
In the philosophy of science, models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge.
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Named set theory
Named set theory is a branch of theoretical mathematics that studies the structures of names.
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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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Ordered field
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.
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Oriented matroid
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partially ordered vector spaces).
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Outline of logic
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics.
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Paradoxes of set theory
This article contains a discussion of paradoxes of set theory.
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Pedagogical grammar
A pedagogical grammar is a modern approach in linguistics intended to aid in teaching an additional language.
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Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives.
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Point–line–plane postulate
In geometry, the point–line–plane postulate is a collection of assumptions (axioms) that can be used in a set of postulates for Euclidean geometry in two (plane geometry), three (solid geometry) or more dimensions.
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Positivism
Positivism is a philosophical theory stating that certain ("positive") knowledge is based on natural phenomena and their properties and relations.
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Primitive notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
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Quantity calculus
Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities.
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Ratnatraya
Jainism emphasises that ratnatraya (triple gems of Jainism) — the right faith (Samyak Darshana), right knowledge (Samyak Gyana) and right conduct (Samyak Charitra) — constitutes the path to liberation.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Recursion
Recursion occurs when a thing is defined in terms of itself or of its type.
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Relationship between mathematics and physics
The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since Antiquity, and more recently also by historians and educators.
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Richard Balam
Richard Balam (fl. 1653), was an English mathematician.
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Richard von Mises
Richard Edler von Mises (19 April 1883 – 14 July 1953) was a scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory.
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Rigour
Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.
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Russell's paradox
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
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Saccheri–Legendre theorem
In absolute geometry, the Saccheri–Legendre theorem states that the sum of the angles in a triangle is at most 180°.
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Samuil Shatunovsky
Samuil Shatunovsky (Самуил Осипович Шатуновский; 25 March 1859 – 27 March 1929) was a Russian mathematician.
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Scientific modelling
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge.
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Separation axiom
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider.
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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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Skolem's paradox
In mathematical logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem.
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Soundness
In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
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Stevens's power law
Stevens's power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength.
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Substitution (logic)
Substitution is a fundamental concept in logic.
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Suslin's problem
In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.
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Syntactic Structures
Syntactic Structures is a major work in linguistics by American linguist Noam Chomsky.
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Synthetic geometry
Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.
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Tarski's axiomatization of the reals
In 1936, Alfred Tarski set out an axiomatization of the real numbers and their arithmetic, consisting of only the 8 axioms shown below and a mere four primitive notions: the set of reals denoted R, a binary total order over R, denoted by infix This axiomatization does not give rise to a first-order theory, because the formal statement of axiom 3 includes two universal quantifiers over all possible subsets of R. Tarski proved these 8 axioms and 4 primitive notions independent.
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Tautology (logic)
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
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Theory (mathematical logic)
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language.
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Timeline of geometry
A timeline of algebra and geometry.
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Timeline of mathematics
This is a timeline of pure and applied mathematics history.
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Timeline of thermodynamics
A timeline of events related to thermodynamics.
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Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.
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Van Hiele model
In mathematics education, the Van Hiele model is a theory that describes how students learn geometry.
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Von Neumann–Bernays–Gödel set theory
In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel set theory (ZFC).
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Where Mathematics Comes From
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist.
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Whitehead's point-free geometry
In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point.
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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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Axiom system, Axiomatic approach, Axiomatic definition, Axiomatic framework, Axiomatic logic, Axiomatic method, Axiomatic reasoning, Axiomatic theory, Axiomatisation, Axiomatization, Hilbert-style calculi.
References
[1] https://en.wikipedia.org/wiki/Axiomatic_system
