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

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
Keywords Finite set theory  adjunction  substandard model  standard model  hereditarily finite
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DOI 10.1002/malq.200910114
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References found in this work BETA

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.
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.
Induction and Foundation in the Theory of Hereditarily Finite Sets.Flavio Previale - 1994 - Archive for Mathematical Logic 33 (3):213-241.

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