Notre Dame Journal of Formal Logic

On Non-wellfounded Sets as Fixed Points of Substitutions

Tapani Hyttinen and Matti Pauna

Abstract

We study the non-wellfounded sets as fixed points of substitution. For example, we show that ZFA implies that every function has a fixed point. As a corollary we determine for which functions f there is a function g such that $ g = g \star f$. We also present a classification of non-wellfounded sets according to their branching structure.

Article information

Source
Notre Dame J. Formal Logic, Volume 42, Number 1 (2001), 23-40.

Dates
First available in Project Euclid: 30 May 2003

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1054301353

Digital Object Identifier
doi:10.1305/ndjfl/1054301353

Mathematical Reviews number (MathSciNet)
MR1993388

Zentralblatt MATH identifier
1023.03048

Subjects
Primary: 03E30: Axiomatics of classical set theory and its fragments
Secondary: 03E65: Other hypotheses and axioms 03E70: Nonclassical and second-order set theories

Keywords
non-wellfounded sets substitution fixed point

Citation

Hyttinen, Tapani; Pauna, Matti. On Non-wellfounded Sets as Fixed Points of Substitutions. Notre Dame J. Formal Logic 42 (2001), no. 1, 23--40. doi:10.1305/ndjfl/1054301353. https://projecteuclid.org/euclid.ndjfl/1054301353


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References

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  • Marshall, M. V., and M. G. Schwarze, "Rank in set theory without foundation", Archive for Mathematical Logic, vol. 38 (1999), pp. 387–93.