Non‐well‐founded extensions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbf {V}$\end{document} |
| |
Authors: | William R Brian |
| |
Institution: | Mathematical Institute, University of Oxford, 24‐29 St. Giles’, Oxford, OX1 3LB, England |
| |
Abstract: | 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 $\mathsf {ZFC}^-$ in which θ has a non‐degenerate solution. We shall prove that this Mθ is the smallest model for $\mathsf {ZFC}^-$ which contains $\mathbf {V}$ and has a non‐degenerate solution of θ. |
| |
Keywords: | set theory non‐well‐founded anti‐foundation model MSC (2010) 03E70 |
|
|