Substandard models of finite set theory

Mathematical Logic Quarterly 56 (6):631-642 (2010)
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Abstract

A survey of the isomorphic submodels of Vω, the set of hereditarily finite sets. In the usual language of set theory, Vω has 2ℵ0 isomorphic submodels. But other set-theoretic languages give different systems of submodels. For example, the language of adjunction allows only countably many isomorphic submodels of Vω

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10.1002/malq.200910114

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Citations of this work

Ordinal operations on graph representations of sets.Laurence Kirby - 2013 - Mathematical Logic Quarterly 59 (1-2):19-26.

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References found in this work

On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
Finitary Set Theory.Laurence Kirby - 2009 - Notre Dame Journal of Formal Logic 50 (3):227-244.
Induction and foundation in the theory of hereditarily finite sets.Flavio Previale - 1994 - Archive for Mathematical Logic 33 (3):213-241.
Addition and multiplication of sets.Laurence Kirby - 2007 - Mathematical Logic Quarterly 53 (1):52-65.
A hierarchy of hereditarily finite sets.Laurence Kirby - 2008 - Archive for Mathematical Logic 47 (2):143-157.

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