# Sh:912

- Kennedy, J. C., Shelah, S., & Väänänen, J. A. (2008).
*Regular ultrafilters and finite square principles*. J. Symbolic Logic,**73**(3), 817–823. DOI: 10.2178/jsl/1230396748 MR: 2444269 -
Abstract:

We show that many singular cardinals \lambda above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle \square^{fin}_{\lambda, D} introduced in [3]. For such ultrafilters D and cardinals \lambda there are models of size \lambda for which M^{\lambda}/D is not \lambda^{++}-universal and elementarily equivalent models M and N of size \lambda for which M^\lambda/D and N^\lambda/D are non-isomorphic. The question of the existence of such ultrafilters and models was raised in [1]. - Version 2007-08-06_11 (9p) published version (8p)

Bib entry

@article{Sh:912, author = {Kennedy, Juliette Cara and Shelah, Saharon and V{\"a}{\"a}n{\"a}nen, Jouko A.}, title = {{Regular ultrafilters and finite square principles}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {73}, number = {3}, year = {2008}, pages = {817--823}, issn = {0022-4812}, mrnumber = {2444269}, mrclass = {03C20 (03E55)}, doi = {10.2178/jsl/1230396748} }