Axiom Of Adjunction

(Axioms Of Set Theory)


Axioms Of Set Theory since 1937
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What is Axiom of adjunction?

In mathematical set theory, the axiom of adjunction states that for any two sets x, y there is a set w = x ∪ {y} given by "adjoining" the set y to the set x. Bernays ( page 68, axiom II (2)) introduced the axiom of adjunction as one of the axioms for a system of set theory that he introduced in about 1929.It is a weak axiom, used in some weak systems of set theory such as general set theory or . The adjunction operation is also used as one of the operations of primitive recursive set functions. Tarski and Smielew showed that Robinson arithmetic can be interpreted in a weak set theory whose axioms are extensionality, the existence of the empty set, and the axiom of adjunction (p.34).

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