Non-well-founded extensions of documentclass{article}usepackage{amssymb}begin{document}pagestyle{empty}$mathbf {V}$end{document}

• Published in: Mathematical logic quarterly 2013-05, Vol.59 (3), p.167-176
• Main Author: Brian, William R.
• Format: Article
• Language: English
• Subjects: anti-foundation; model MSC 03E70; non-well-founded; set theory; Studies
• ISSN: 0942-5616; 1521-3870
• DOI: 10.1002/malq.201200014

This paper describes a new and user‐friendly method for constructing models of non‐well‐founded set theory. Given a sufficiently well‐behaved system θ of non‐well‐founded set‐theoretic equations, we describe how to construct a model Mθ for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {ZFC}^-$\end{document} in which θ has a non‐degenerate solution. We shall prove that this Mθ is the smallest model for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {ZFC}^-$\end{document} which contains \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbf {V}$\end{document} and has a non‐degenerate solution of θ.