# Sh:852

• Kennedy, J. C., & Shelah, S. (2004). More on regular reduced products. J. Symbolic Logic, 69(4), 1261–1266.
• Abstract:
The authors show, by means of a finitary version \square^{fin}_{\lambda,D} of the combinatorial principle \square^{b^*}_{\lambda}, the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal \lambda, if M_i and N_i are elementarily equivalent models of a language of size \le\lambda, then the second player has a winning strategy in the Ehrenfeucht-Fraı̈ssé game of length \lambda^+ on \prod_i M_i/D and \prod_i N_i/D. If in addition 2^{\lambda}=\lambda^+ and i<\lambda implies |M_i|+|N_i|\leq \lambda^+ this means that the ultrapowers are isomorphic.
• Current version: 2006-11-30_10 (9p) published version (7p)
Bib entry
@article{Sh:852,
author = {Kennedy, Juliette Cara and Shelah, Saharon},
title = {{More on regular reduced products}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {69},
number = {4},
year = {2004},
pages = {1261--1266},
issn = {0022-4812},
mrnumber = {2135667},
mrclass = {03C20 (03E35 03E55)},
doi = {10.2178/jsl/1102022222},
note = {\href{https://arxiv.org/abs/math/0504200}{arXiv: math/0504200}},
arxiv_number = {math/0504200}
}