Superclub, splitting, separating statements

Shimon Garti; Saharon Shelah

doi:10.1007/s10998-025-00628-2

Superclub, splitting, separating statements

Shimon Garti, Saharon Shelah

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

Abstract

We prove that superclub implies s=ω1. More generally, if κ is weakly compact then superclub implies sκ=κ+. Based on this statement, we separate tiltan from superclub at successors of supercompact cardinals. We also use the Galvin property in order to separate tiltan from superclub at both successors of regular and successors of singular cardinals.

Original language	English
Pages (from-to)	217-227
Number of pages	11
Journal	Periodica Mathematica Hungarica
Volume	90
Issue number	2
DOIs	https://doi.org/10.1007/s10998-025-00628-2
State	Published - 1 Jun 2025
Externally published	Yes

Keywords

Splitting number
Superclub
The Galvin property
Tiltan
Weakly compact cardinals

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s10998-025-00628-2

Cite this

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N2 - We prove that superclub implies s=ω1. More generally, if κ is weakly compact then superclub implies sκ=κ+. Based on this statement, we separate tiltan from superclub at successors of supercompact cardinals. We also use the Galvin property in order to separate tiltan from superclub at both successors of regular and successors of singular cardinals.

AB - We prove that superclub implies s=ω1. More generally, if κ is weakly compact then superclub implies sκ=κ+. Based on this statement, we separate tiltan from superclub at successors of supercompact cardinals. We also use the Galvin property in order to separate tiltan from superclub at both successors of regular and successors of singular cardinals.

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KW - The Galvin property

KW - Tiltan

KW - Weakly compact cardinals

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Superclub, splitting, separating statements

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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