Stably Measurable Cardinals

P D Welch

doi:10.1017/jsl.2019.82

Stably Measurable Cardinals

P D Welch

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Abstract

We define a weak iterability notion that is sufficient for a number of arguments concerning Σ_1-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second uniform indiscernible for bounded subsets of kappa : u_2(kappa ), and secondly to give the consistency strength of a property of Lücke’s.

Original language	English
Pages (from-to)	448 - 470
Number of pages	22
Journal	Journal of Symbolic Logic
Volume	86
Issue number	2
Early online date	15 Jun 2020
DOIs	https://doi.org/10.1017/jsl.2019.82
Publication status	E-pub ahead of print - 15 Jun 2020

Keywords

inner model
large cardinals
reflection principle

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10.1017/jsl.2019.82

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/stably-measurable-cardinals/F874CE2A1AEB3976CAB71E88C7927236. Please refer to any applicable terms of use of the publisher.
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AB - We define a weak iterability notion that is sufficient for a number of arguments concerning Σ_1-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second uniform indiscernible for bounded subsets of kappa : u_2(kappa ), and secondly to give the consistency strength of a property of Lücke’s.

KW - inner model

KW - large cardinals

KW - reflection principle

U2 - 10.1017/jsl.2019.82

DO - 10.1017/jsl.2019.82

M3 - Article (Academic Journal)

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JO - Journal of Symbolic Logic

JF - Journal of Symbolic Logic

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ER -

Stably Measurable Cardinals

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Keywords

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