The first omitting cardinal for Magidority

Shimon Garti; Yair Hayut

doi:https://doi.org/10.1002/malq.201800026

The first omitting cardinal for Magidority

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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 - 1 May 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Logic

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https://doi.org/10.1002/malq.201800026

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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.",

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The first omitting cardinal for Magidority

Abstract

All Science Journal Classification (ASJC) codes

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