# Sh:518

- Laskowski, M. C., & Shelah, S. (1996).
*Forcing isomorphism. II*. J. Symbolic Logic,**61**(4), 1305–1320. arXiv: math/0011169 DOI: 10.2307/2275818 MR: 1456109 -
Abstract:

If T has only countably many complete types, yet has a type of infinite multiplicity then there is a ccc 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 ccc forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if “ccc” is replaced 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. - Version 2000-11-01_10 (23p) published version (17p)

Bib entry

@article{Sh:518, author = {Laskowski, Michael Chris and Shelah, Saharon}, title = {{Forcing isomorphism. II}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {61}, number = {4}, year = {1996}, pages = {1305--1320}, issn = {0022-4812}, mrnumber = {1456109}, mrclass = {03C45 (03C55 03E40)}, doi = {10.2307/2275818}, note = {\href{https://arxiv.org/abs/math/0011169}{arXiv: math/0011169}}, arxiv_number = {math/0011169} }