On the cofinality of ultrapowers
Abstract
All ultrafilters under consideration here are nonprincipal ultrafilters on the set omega of natural numbers. We are concerned with the possible cofinalities of ultrapowers of omega with respect to such ultrafilters. We show that no cardinal below the groupwise density number g can occur as such a cofinality and that at most one cardinal below the splitting number s can so occur. The proof for s, when combined with a result of Nyikos, gives the additional information that all P_{kappa}point ultrafilters, for kappa greater than the bounding number b, are nearly coherent.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1996
 DOI:
 10.48550/arXiv.math/9611210
 arXiv:
 arXiv:math/9611210
 Bibcode:
 1996math.....11210B
 Keywords:

 Mathematics  Logic