# Sh:852

- Kennedy, J. C., & Shelah, S. (2004).
*More on regular reduced products*. J. Symbolic Logic,**69**(4), 1261–1266. arXiv: math/0504200 DOI: 10.2178/jsl/1102022222 MR: 2135667 -
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. - 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}, doi = {10.2178/jsl/1102022222}, mrclass = {03C20 (03E35 03E55)}, mrnumber = {2135667}, mrreviewer = {Pierre Matet}, doi = {10.2178/jsl/1102022222}, note = {\href{https://arxiv.org/abs/math/0504200}{arXiv: math/0504200}}, arxiv_number = {math/0504200} }