# Sh:912

• Kennedy, J. C., Shelah, S., & Väänänen, J. A. (2008). Regular ultrafilters and finite square principles. J. Symbolic Logic, 73(3), 817–823.
• 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].
• Current version: 2007-08-06_10 (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}
}