English

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}
}