Non-Well-Foundedness

Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 159)

Abstract

A non-well-founded set theory belongs to axiomatic set theories that violate the rule of well-foundedness and, as an example, allow sets to contain themselves: \(X\in X\). In non-well-founded set theories, the foundation axiom of Zermelo-Fraenkel set theory is replaced by axioms implying its negation.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Information Technology and Management in RzeszowRzeszówPoland
  2. 2.Department of Computer Science, Faculty of Mathematics and Natural SciencesUniversity of RzeszówRzeszówPoland

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