Faster access than browser!Similarities between Morse–Kelley set theory and New Foundations
Morse–Kelley set theory and New Foundations have 23 things in common (in Unionpedia): Axiom of choice, Axiom of extensionality, Axiom schema of specification, Bijection, Binary relation, Cardinal number, Class (set theory), Function (mathematics), Impredicativity, Injective function, Ordered pair, Ordinal number, Peano axioms, Power set, Set theory, Singleton (mathematics), Transfinite induction, Urelement, Von Neumann universe, Von Neumann–Bernays–Gödel set theory, Well-order, Willard Van Orman Quine, Zermelo–Fraenkel set theory.
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.
Axiom of choice and Morse–Kelley set theory · Axiom of choice and New Foundations ·
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.
Axiom of extensionality and Morse–Kelley set theory · Axiom of extensionality and New Foundations ·
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.
Axiom schema of specification and Morse–Kelley set theory · Axiom schema of specification and New Foundations ·
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
Bijection and Morse–Kelley set theory · Bijection and New Foundations ·
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.
Binary relation and Morse–Kelley set theory · Binary relation and New Foundations ·
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
Cardinal number and Morse–Kelley set theory · Cardinal number and New Foundations ·
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.
Class (set theory) and Morse–Kelley set theory · Class (set theory) and New Foundations ·
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
Function (mathematics) and Morse–Kelley set theory · Function (mathematics) and New Foundations ·
Impredicativity
Something that is impredicative, in mathematics and logic, is a self-referencing definition.
Impredicativity and Morse–Kelley set theory · Impredicativity and New Foundations ·
Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
Injective function and Morse–Kelley set theory · Injective function and New Foundations ·
Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
Morse–Kelley set theory and Ordered pair · New Foundations and Ordered pair ·
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.
Morse–Kelley set theory and Ordinal number · New Foundations and Ordinal number ·
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
Morse–Kelley set theory and Peano axioms · New Foundations and Peano axioms ·
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, đť’«(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
Morse–Kelley set theory and Power set · New Foundations and Power set ·
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
Morse–Kelley set theory and Set theory · New Foundations and Set theory ·
Singleton (mathematics)
In mathematics, a singleton, also known as a unit set, is a set with exactly one element.
Morse–Kelley set theory and Singleton (mathematics) · New Foundations and Singleton (mathematics) ·
Transfinite induction
Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.
Morse–Kelley set theory and Transfinite induction · New Foundations and Transfinite induction ·
Urelement
In set theory, a branch of mathematics, an urelement or ur-element (from the German prefix ur-, 'primordial') is an object (concrete or abstract) that is not a set, but that may be an element of a set.
Morse–Kelley set theory and Urelement · New Foundations and Urelement ·
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.
Morse–Kelley set theory and Von Neumann universe · New Foundations and Von Neumann universe ·
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).
Morse–Kelley set theory and Von Neumann–Bernays–Gödel set theory · New Foundations and Von Neumann–Bernays–Gödel set theory ·
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.
Morse–Kelley set theory and Well-order · New Foundations and Well-order ·
Willard Van Orman Quine
Willard Van Orman Quine (known to intimates as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century." From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement.
Morse–Kelley set theory and Willard Van Orman Quine · New Foundations and Willard Van Orman Quine ·
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.
Morse–Kelley set theory and Zermelo–Fraenkel set theory · New Foundations and Zermelo–Fraenkel set theory ·
The list above answers the following questions
- What Morse–Kelley set theory and New Foundations have in common
- What are the similarities between Morse–Kelley set theory and New Foundations
Morse–Kelley set theory and New Foundations Comparison
Morse–Kelley set theory has 79 relations, while New Foundations has 75. As they have in common 23, the Jaccard index is 14.94% = 23 / (79 + 75).
References
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