Notre Dame Journal of Formal Logic

On Non-wellfounded Sets as Fixed Points of Substitutions

Tapani Hyttinen and Matti Pauna


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

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

First available in Project Euclid: 30 May 2003

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Zentralblatt MATH identifier

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

non-wellfounded sets substitution fixed point


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.

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