More on regular reduced products
Abstract
The authors show, by means of a finitary version squarefinlambda,D of the combinatorial principle squareb*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 Mi and Ni 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 prodi Mi/D and prodi Ni/D. If in addition 2lambda= lambda+ and i<lambda implies |Mi|+|Ni| <= lambda+ this means that the ultrapowers are isomorphic.
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