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Expressing infinity without foundation

Published online by Cambridge University Press:  12 March 2014

Franco Parlamento  and
Alberto Policriti
Franco Parlamento
Affiliation:
Dipartimento di Matematica e Informatica, Università di Udine, 33100 Udine, Italy
Alberto Policriti
Affiliation:
Dipartimento di Matematica e Informatica, Università di Udine, 33100 Udine, Italy Computer Science Department, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
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Abstract

The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1230 - 1235
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

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[CFO90]Cantone, D., Ferro, A., and Omodeo, E., Computable set theory, Oxford University Press, Oxford, 1990.Google Scholar
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[PP88]Parlamento, F. and Policriti, A., The logically simplest form of the infinity axiom, Proceedings of the American Mathematical Society, vol. 103 (1988), pp. 274–276.CrossRefGoogle Scholar
[PP90a]Parlamento, F. and Policriti, A., The decision problem for restricted universal quantification in set theory and the axiom of foundation, Technical Report, Dipartimento di Matematica e Informatica, Università di Udine, Udine, 1990.Google Scholar
[PP90b]Parlamento, F. and Policriti, A., Note on “The logically simplest form of the infinity axiom”, Proceedings of the American Mathematical Society, vol. 108 (1990), pp. 285–286.Google Scholar