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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.42 (2010)
  6. Stating Infinity in Set/Hyperset Theory
 
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Stating Infinity in Set/Hyperset Theory

Omodeo, Eugenio G.
•
Policriti, Alberto
•
Tomescu, Alexandru I.
2010
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ISSN
0049-4704
http://hdl.handle.net/10077/3891
  • Article

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.
Subjects
  • Satisfiability

  • Decision Algorithms

  • Infinity Axiom

  • Computable Set Theory...

  • Non-Well-Founded Sets...

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
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 (2010)
Languages
en
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