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A theorem on the isomorphism property

Published online by Cambridge University Press:  12 March 2014

Renling Jin
Renling Jin*
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, E-mail: jin@math.wisc.edu
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Abstract

An -structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in are internal. A nonstandard universe is said to satisfy the κ-isomorphism property if for any two internally presented -structures and , where has less than κ many symbols, is elementarily equivalent to implies that is isomorphic to . In this paper we prove that the ℵ1-isomorphism property is equivalent to the ℵ0-isomorphism property plus ℵ1-saturation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 3 , September 1992 , pp. 1011 - 1017
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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