Regularity of ultrafilters and the core model
type: Item
instance of: scholarly article
title: Regularity of ultrafilters and the core model
zbMATH Open document ID: 0663.03037
DOI: 10.1007/BF02778036
author: Hans-Dieter Donder
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: This paper contains the following two important results: (1) If there is no model with a measurable cardinal, then every uniform ultrafilter on a singular cardinal is regular. (2) If there is no inner model with a measurable cardinal and \(\kappa >\omega\) is regular with \((\kappa^+)^ K=\kappa^+\), then every uniform ultrafilter on \(\kappa\) is regular. (So in particular, in the core model K, every uniform ultrafilter is regular.) The author introduces certain combinatorial principles, which are strengthenings of \(\square_{\kappa}\). He shows these hold in K. Then from these combinatorial statements he proves the results about uniform ultrafilters.
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 4083612
zbMATH Keywords: regular ultrafilter
zbMATH Keywords: model with a measurable cardinal
zbMATH Keywords: uniform ultrafilter
zbMATH Keywords: singular cardinal
zbMATH Keywords: inner model
zbMATH Keywords: core model
zbMATH Keywords: combinatorial principles
reviewed by: Neil H. Williams
MaRDI profile type: Publication
cites work: Regularity of ultrafilters
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cites work: Model theory
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cites work: The core model
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cites work: The fine structure of the constructible hierarchy
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cites work: Strong axioms of infinity and elementary embeddings
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cites work: On the Existence of Nonregular Ultrafilters and the Cardinality of Ultrapowers
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cites work: On a problem of Gillman and Keisler
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description: scientific article; zbMATH DE number 4083612