Journal of Symbolic Logic

Forcing Isomorphism II

M. C. Laskowski and S. Shelah

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


If $T$ has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion $\mathscr{Q}$ such that, in any $\mathscr{Q}$-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.

Article information

J. Symbolic Logic, Volume 61, Issue 4 (1996), 1305-1320.

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Laskowski, M. C.; Shelah, S. Forcing Isomorphism II. J. Symbolic Logic 61 (1996), no. 4, 1305--1320.

Export citation