STATIONARY REFLECTION and the FAILURE of the SCH

Omer Ben-Neria; Yair Hayut; Spencer Unger

doi:https://doi.org/10.1017/jsl.2023.80

STATIONARY REFLECTION and the FAILURE of the SCH

Omer Ben-Neria, Yair Hayut, Spencer Unger

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and every collection of fewer than stationary subsets of reflects simultaneously. For >, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Journal of Symbolic Logic
Volume	89
Issue number	1
DOIs	https://doi.org/10.1017/jsl.2023.80
State	Published - 27 Mar 2024

Keywords

Prikry forcing
SCH.
stationary reflection

All Science Journal Classification (ASJC) codes

Logic
Philosophy

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https://doi.org/10.1017/jsl.2023.80

Cite this

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abstract = "In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and every collection of fewer than stationary subsets of reflects simultaneously. For >, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.",

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AU - Hayut, Yair

AU - Unger, Spencer

N1 - Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

PY - 2024/3/27

Y1 - 2024/3/27

N2 - In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and every collection of fewer than stationary subsets of reflects simultaneously. For >, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.

AB - In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and every collection of fewer than stationary subsets of reflects simultaneously. For >, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.

KW - Prikry forcing

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KW - stationary reflection

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M3 - مقالة

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JO - Journal of Symbolic Logic

JF - Journal of Symbolic Logic

IS - 1

ER -

STATIONARY REFLECTION and the FAILURE of the SCH

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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