On the cofinality of the least λ-strongly compact cardinal

Zhixing You; Jiachen Yuan

doi:10.1017/jsl.2023.4

On the cofinality of the least λ-strongly compact cardinal

Zhixing You, Jiachen Yuan

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

Abstract

In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ-strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ-strongly compact cardinal always carries a λ-complete uniform ultrafilter.

Original language	English
Journal	Journal of Symbolic Logic
Early online date	19 Jan 2023
DOIs	https://doi.org/10.1017/jsl.2023.4
Publication status	E-pub ahead of print - 19 Jan 2023

Keywords

Cofinality
Iterated ultrapower
Radin forcing
λ-strongly compact cardinal

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10.1017/jsl.2023.4

on-the-cofinality-of-the-least-l-strongly-compact-cardinalAccepted author manuscript, 465 KB

Cite this

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title = "On the cofinality of the least λ-strongly compact cardinal",

abstract = "In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ-strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ-strongly compact cardinal always carries a λ-complete uniform ultrafilter.",

keywords = "Cofinality, Iterated ultrapower, Radin forcing, λ-strongly compact cardinal",

author = "Zhixing You and Jiachen Yuan",

note = "Funding Information: During the work, the first author was supported by NSFC No. 11871464 until July 2022 and the China Scholarship Council (No. 202004910742) from October 2020 to October 2021. The first author was also supported by the European Research Council (grant agreement ERC-2018-StG 802756) from July 2022. The second author was supported by UKRI Future Leaders Fellowship [MR/T021705/2]. ",

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AU - Yuan, Jiachen

N1 - Funding Information: During the work, the first author was supported by NSFC No. 11871464 until July 2022 and the China Scholarship Council (No. 202004910742) from October 2020 to October 2021. The first author was also supported by the European Research Council (grant agreement ERC-2018-StG 802756) from July 2022. The second author was supported by UKRI Future Leaders Fellowship [MR/T021705/2].

PY - 2023/1/19

Y1 - 2023/1/19

N2 - In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ-strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ-strongly compact cardinal always carries a λ-complete uniform ultrafilter.

AB - In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ-strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ-strongly compact cardinal always carries a λ-complete uniform ultrafilter.

KW - Cofinality

KW - Iterated ultrapower

KW - Radin forcing

KW - λ-strongly compact cardinal

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JO - Journal of Symbolic Logic

JF - Journal of Symbolic Logic

SN - 0022-4812

ER -

On the cofinality of the least λ-strongly compact cardinal

Abstract

Keywords

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Understanding the axioms: the interactions of the Axiom of Choice with large cardinal axioms

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On the cofinality of the least λ-strongly compact cardinal

Abstract

Keywords

Access to Document

Other files and links

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Understanding the axioms: the interactions of the Axiom of Choice with large cardinal axioms

Cite this