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Stating Infinity in Set/Hyperset Theory
Omodeo, Eugenio G.
Policriti, Alberto
Tomescu, Alexandru I.
2010
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 (2010)
Publisher
EUT Edizioni Università di Trieste
Source
Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu, "Stating Infinity in Set/Hyperset Theory", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 42 (2010), pp. 205-210.
Languages
en
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