Sigma-Prikry forcing III: Down to ℵω

Alejandro Poveda; Assaf Rinot; Dima Sinapova

doi:10.1016/j.aim.2023.109377

Sigma-Prikry forcing III: Down to ℵ_ω

Alejandro Poveda
, Assaf Rinot
, Dima Sinapova

Department of Mathematics

Harvard University
Rutgers - The State University of New Jersey, New Brunswick

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

1 Scopus citations

Abstract

We prove the consistency of the failure of the singular cardinals hypothesis at ℵ_ω together with the reflection of all stationary subsets of ℵ_ω+1. This shows that two classical results of Magidor (from 1977 and 1982) can hold simultaneously.

Original language	English
Article number	109377
Journal	Advances in Mathematics
Volume	435
DOIs	https://doi.org/10.1016/j.aim.2023.109377
State	Published - 15 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Funding

Poveda was supported by postdoctoral fellowships from the Einstein Institute of Mathematics ( Hebrew University of Jerusalem ) and from the Center of Mathematical Sciences and Applications, Harvard University ). Rinot was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756 ) and by the Israel Science Foundation (grant agreement 203/22 ). Sinapova was partially supported by the National Science Foundation , Career-1454945 and DMS-1954117 .

Funders	Funder number
Einstein Institute of Mathematics
National Science Foundation	DMS-1954117
Harvard University
European Commission	ERC-2018-StG 802756
Israel Science Foundation	203/22

Keywords

Iterated forcing
Sigma-Prikry forcing
Singular cardinals hypothesis
Stationary reflection

Access to Document

10.1016/j.aim.2023.109377

Cite this

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