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18 relations: Axiom of choice, Axiom of extensionality, Axiom schema of predicative separation, Axiom schema of specification, Bijection, Choice function, Constructive set theory, Dedekind-infinite set, Errett Bishop, Finite set, Heyting arithmetic, Intuitionistic type theory, John Myhill, Law of excluded middle, Mathematical logic, Natural number, Proposition, Set-builder notation.
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 schema of predicative separation
In axiomatic set theory, the axiom schema of predicative separation, or of restricted, or Δ0 separation, is a schema of axioms which is a restriction of the usual axiom schema of separation in Zermelo–Fraenkel set theory.
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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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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.
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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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Constructive set theory
Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.
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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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Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an American mathematician known for his work on analysis.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Heyting arithmetic
In mathematical logic, Heyting arithmetic (sometimes abbreviated HA) is an axiomatization of arithmetic in accordance with the philosophy of intuitionism (Troelstra 1973:18).
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Intuitionistic type theory
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.
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John Myhill
John R. Myhill Sr. (11 August 1923 – 15 February 1987) was a British mathematician.
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Law of excluded middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true.
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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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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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Proposition
The term proposition has a broad use in contemporary analytic philosophy.
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Set-builder notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.
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Diaconescu theorem, Diaconescu-Goodman-Myhill theorem, Diaconescu–Goodman–Myhill theorem, Goodman-Myhill theorem, Goodman-Myhill-Diaconescu theorem, Goodman–Myhill theorem, Goodman–Myhill–Diaconescu theorem.
