Superclub, splitting, separating statements

Shimon Garti; Saharon Shelah

doi:10.1007/s10998-025-00628-2

Superclub, splitting, separating statements

Shimon Garti^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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 - Jun 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Splitting number
Superclub
The Galvin property
Tiltan
Weakly compact cardinals

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10.1007/s10998-025-00628-2

Cite this

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Superclub, splitting, separating statements

Abstract

Bibliographical note

Keywords

Access to Document

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