### Regular Ultrafilters and Finite Square Principles

by Kennedy and Shelah and Vaananen. [KShV:912]

J Symbolic Logic, 2008

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].

Back to the list of publications