The first omitting cardinal for Magidority

Shimon Garti; Yair Hayut

doi:10.1002/malq.201800026

The first omitting cardinal for Magidority

Shimon Garti, Yair Hayut^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

An infinite cardinal λ is Magidor if and only if (Formula presented.). It is known that if λ is Magidor then (Formula presented.) for some α < λ, and the first such α is denoted by α _m (λ). In this paper we try to understand some of the properties of α _m (λ). We prove that α _m (λ) can be the successor of a supercompact cardinal, when λ is a Magidor cardinal. From this result we obtain the consistency of α _m (λ) being a successor of a singular cardinal with uncountable cofinality.

Original language	American English
Pages (from-to)	95-104
Number of pages	10
Journal	Mathematical Logic Quarterly
Volume	65
Issue number	1
DOIs	https://doi.org/10.1002/malq.201800026
State	Published - May 2019

Bibliographical note

Funding Information:
Acknowledgements First author’s research is supported by Shelah’s ERC grant 338821. We should like to thank the anonymous referee for many helpful suggestions that improved this paper’s readability and correctness.

Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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10.1002/malq.201800026

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The first omitting cardinal for Magidority

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