It is known that the Infinity Axiom can be expressed, even if the Axiom of Foundation is not assumed, in a logically simple form, by means of a formula involving only restricted universal quantifiers. Moreover, with Aczel’s Anti-Foundation Axiom superseding von Neumann’s Axiom of Foundation, a similar formula has recently emerged, which enjoys the additional property that it is satisfied only by (infinite) ill-founded sets. We give here new short proofs of both results.
Stating infinity in set/hyperset theories / Omodeo, Eugenio; Policriti, A.; Tomescu, A. I.. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - STAMPA. - 42:(2010), pp. 211-234.
Stating infinity in set/hyperset theories
OMODEO, EUGENIO;
2010-01-01
Abstract
It is known that the Infinity Axiom can be expressed, even if the Axiom of Foundation is not assumed, in a logically simple form, by means of a formula involving only restricted universal quantifiers. Moreover, with Aczel’s Anti-Foundation Axiom superseding von Neumann’s Axiom of Foundation, a similar formula has recently emerged, which enjoys the additional property that it is satisfied only by (infinite) ill-founded sets. We give here new short proofs of both results.Pubblicazioni consigliate
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