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Forcing isomorphism II

Published online by Cambridge University Press:  12 March 2014

M. C. Laskowski
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA, E-mail:
S. Shelah
School of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail:


If T has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion such that, in any -generic extension of the universe, there are non-isomorphic models M1 and M2 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.

Research Article
Copyright © Association for Symbolic Logic 1996

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