Forcing isomorphism II

Journal of Symbolic Logic 61 (4):1305-1320 (1996)
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Abstract

If T has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion Q such that, in any Q-generic extension of the universe, there are non-isomorphic models M 1 and M 2 of T that can be forced isomorphic by a c.c.c. forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if `c.c.c.' is replaced by other cardinal-preserving adjectives. We also give an example showing that membership in a pseudo-elementary class can be altered by very simple cardinal-preserving forcings

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Stability in Model Theory.Daniel Lascar & J. E. Wallington - 1990 - Journal of Symbolic Logic 55 (2):881-883.

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