Journal of Symbolic Logic

Forcing Isomorphism II

M. C. Laskowski and S. Shelah

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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 $\mathscr{Q}$ 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

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745137

Mathematical Reviews number (MathSciNet)
MR1456109

Zentralblatt MATH identifier
0878.03020

JSTOR
links.jstor.org

Citation

Laskowski, M. C.; Shelah, S. Forcing Isomorphism II. J. Symbolic Logic 61 (1996), no. 4, 1305--1320. https://projecteuclid.org/euclid.jsl/1183745137


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