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searching for Inductive set 7 found (11 total)

Morse–Kelley set theory (3,123 words) [view diff] exact match in snippet view article find links to article

y\,(x\in y\land y\in a)])\rightarrow Ms].} Infinity: There exists an inductive set y, meaning that (i) the empty set is a member of y; (ii) if x is a member

ST type theory (944 words) [view diff] exact match in snippet view article find links to article

literature does not explain why the usual axiom of infinity (there exists an inductive set) of ZFC of other set theories could not be married to ST. ST reveals

Well-ordering principle (1,144 words) [view diff] exact match in snippet view article find links to article

axiomatic set theory, the natural numbers are defined as the smallest inductive set (i.e., set containing 0 and closed under the successor operation). One

New Foundations (8,107 words) [view diff] exact match in snippet view article find links to article

trivially true, since the universal set V {\displaystyle V} would be an inductive set. Since inductive sets always exist, the set of natural numbers N {\displaystyle

Natural number (5,898 words) [view diff] exact match in snippet view article find links to article

to be inductive. The intersection of all inductive sets is still an inductive set. This intersection is the set of the natural numbers. It follows that

Scott–Potter set theory (1,846 words) [view diff] exact match in snippet view article find links to article

necessarily finite. For mathematical purposes, the axiom "There exists an inductive set" would suffice. The following statements, while in the nature of axioms

Constructive set theory (34,301 words) [view diff] exact match in snippet view article find links to article

aim of the axiom of infinity is to eventually obtain unique smallest inductive set. In the context of common set theory axioms, one statement of infinitude