Unifying some notions of infnity in ZC and ZF
Unifying some notions of infnity in ZC and ZF
Author(s): Greg OmanSubject(s): Philosophy, Logic
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego
Summary/Abstract: Let ZC - I (respectively, ZF - I) be the theory obtained by deleting the axiom of innity 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 innite set.
Journal: Reports on Mathematical Logic
- Issue Year: 2016
- Issue No: 51
- Page Range: 43-56
- Page Count: 14
- Language: English