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ON PRODUCTS OF ULTRAFILTERS

Part of: Set theory

Published online by Cambridge University Press:  09 June 2025

GABRIEL GOLDBERG
GABRIEL GOLDBERG*
Affiliation:
UC BERKELEY, EVANS HALL UNIVERSITY DRIVE BERKELEY, CA 94720 USA
*
E-mail: ggoldberg@berkeley.edu
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Abstract

Assuming the Generalized Continuum hypothesis, this paper answers the question: when is the tensor product of two ultrafilters equal to their Cartesian product? It is necessary and sufficient that their Cartesian product is an ultrafilter; that the two ultrafilters commute in the tensor product; that for all cardinals $\lambda $, one of the ultrafilters is both $\lambda $-indecomposable and $\lambda ^+$-indecomposable; that the ultrapower embedding associated with each ultrafilter restricts to a definable embedding of the ultrapower of the universe associated with the other.

Keywords

UltrafiltersproductsKetonen orderinternal relation

MSC classification

Primary: 03E05: Other combinatorial set theory 03E55: Large cardinals

Information

Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 17
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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