More on regular reduced products
Logic
2007-05-23 v1
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 <= lambda, then the second player has a winning strategy in the Ehrenfeucht-Fraisse 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| <= lambda^+ this means that the ultrapowers are isomorphic.
Keywords
Cite
@article{arxiv.math/0504200,
title = {More on regular reduced products},
author = {Juliette Kennedy and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0504200},
year = {2007}
}