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].

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