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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