Generic families and models of set theory with the axiom of choice
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- by Krzysztof Ciesielski and Wojciech Guzicki PDF
- Proc. Amer. Math. Soc. 106 (1989), 199-206 Request permission
Abstract:
Let $M$ be a countable transitive model of ZFC and $A$ be a countable $M$-generic family of Cohen reals. We prove that there is no smallest transitive model $N$ of ZFC that either $M \cup A \subseteq N$ or $M \cup \{ A\} \subseteq N$. It is also proved that there is no smallest transitive model $N$ of ZFC$^{-}$ (ZFC theory without the power set axiom) such that $M \cup \{ A\} \subseteq N$. It is also proved that certain classes of extensions of $M$ obtained by Cohen generic reals have no minimal model.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 199-206
- MSC: Primary 03C62; Secondary 03E25
- DOI: https://doi.org/10.1090/S0002-9939-1989-0994389-8
- MathSciNet review: 994389