A theorem on the isomorphism property

Journal of Symbolic Logic 57 (3):1011-1017 (1992)
Abstract
An L-structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in L are internal. A nonstandard universe is said to satisfy the κ-isomorphism property if for any two internally presented L-structures U and B, where L has less than κ many symbols, U is elementarily equivalent to B implies that U is isomorphic to B. In this paper we prove that the ℵ1-isomorphism property is equivalent to the ℵ0-isomorphism property plus ℵ1-saturation
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DOI 10.2307/2275446
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Combinatorial Principles in Nonstandard Analysis.Mauro Di Nasso & Karel Hrbacek - 2003 - Annals of Pure and Applied Logic 119 (1-3):265-293.

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