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Title: Stating Infinity in Set/Hyperset Theory
Authors: Omodeo, Eugenio G.
Policriti, Alberto
Tomescu, Alexandru I.
Keywords: SatisfiabilityDecision AlgorithmsInfinity AxiomComputable Set TheoryNon-Well-Founded Sets
Issue Date: 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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 (2010)
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.
Type: Article
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.42 (2010)

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