A connection between decomposable ultrafilters and possible cofinalities. II

Details A connection between decomposable ultrafilters and possible cofinalities. II A connection between decomposable ultrafilters and possible cofinalities. II

2006-04-30

arxiv.org/abs/math/0605022v1

Published as "Decomposable ultrafilters and possible cofinalities" on Notre Dame Journal of Formal Logic 49, 307--312 (2008).

Mathematics

Logic

6 pages

Scientific paper

We use Shelah's theory of possible cofinalities in order to solve a problem about ultrafilters. THEOREM. Suppose that $ \lambda $ is a singular cardinal, $ \lambda ' < \lambda $, and the ultrafilter $D$ is $ \kappa $-decomposable for all regular cardinals $ \kappa $ with $ \lambda ' < \kappa < \lambda $. Then $D$ is either $ \lambda $-decomposable, or $ \lambda ^+$-decomposable. We give applications to topological spaces and to abstract logics.

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