## Journal of Symbolic Logic

### Forcing Isomorphism II

#### 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 $\mathscr{Q}$ 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

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745137

Mathematical Reviews number (MathSciNet)
MR1456109

Zentralblatt MATH identifier
0878.03020

JSTOR