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A theorem on the isomorphism property

  • Renling Jin (a1)


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.



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