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 . 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 .
Fields of Science
- 111 Mathematics