Unifying some notions of infnity in ZC and ZF
Unifying some notions of infnity in ZC and ZF

Summary/Abstract: Let ZC - I (respectively, ZF - I) be the theory obtained by deleting the axiom of innity from the usual list of axioms for Zermelo set theory with choice (respectively, the usual list of axioms for Zermelo-Fraenkel set theory). In this note, we present a collection of sentences 9x'(x) for which (ZC - I) + 9x'(x) (respectively, (ZF - I)+9x'(x)) proves the existence of an innite set.

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