The isomorphism property for nonstandard universes

Publisher： Cambridge University Press

E-ISSN： 1943-5886|60|2|512-516

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.60, Iss.2, 1995-06, pp. : 512-516

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Abstract

The κ-isomorphism property (IP κ ) for nonstandard universes was introduced by Henson in [4]. There has been some recent effort aimed at more fully understanding this property. Jin and Shelah in [7] have shown that for κ < ⊐ ω , IP κ is equivalent to what we will refer to as the κ-resplendence property. Earlier, in [6], Jin asked if IP κ is equivalent to IPℵ0 plus κ-saturation. He answered this question positively for κ = ℵ1. In this note we extend this answer to all κ. We also extend the result of Jin and Shelah to all κ. (Jin also observed this could be done.)

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