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)

@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}
}