MATHEMATICAL LOGIC QUARTERLY www.mlq-journal.org A Journal for Mathematical Logic, Foundations of Mathematics, and Logical Aspects of Theoretical Computer Science M L Q Editors Armin Hemmerling, Greifswald (Managing) Klaus Ambos-Spies, HeidelbergK laus Me

Abstract

A survey of the isomorphic submodels of Vω, the set of hereditarily finite sets. In the usual language of set theory, Vω has 2 ℵ 0 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