On the cofinality of ultrapowers

Author:

Blass Andreas,Mildenberger Heike

Abstract

AbstractWe prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve three cardinal characteristics of the continuum, the splitting numbers, the unsplitting numberr, and the groupwise density numberg. We also prove some related results for reduced powers with respect to filters other than ultrafilters.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference11 articles.

1. Families of sets and functions;Solomon;Czechoslovak Mathematical Journal,1977

2. Non-isomorphic hyper-real fields from non-isomorphic ultrapowers

3. Countable ultraproducts without CH

4. Canjar R. M. , Model-Theoretic Properties of Countable Ultraproducts Without the Continuum Hypothesis, Ph.D. thesis , University of Michigan, 1982.

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