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
Journal	Periodica Mathematica Hungarica
DOIs	https://doi.org/10.1007/s10998-025-00628-2
State	Accepted/In press - 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Splitting number
Superclub
The Galvin property
Tiltan
Weakly compact cardinals

Access to Document

10.1007/s10998-025-00628-2

Cite this

@article{e9b35764b2f94103b975e7fa5c960488,

title = "Superclub, splitting, separating statements",

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.",

keywords = "Splitting number, Superclub, The Galvin property, Tiltan, Weakly compact cardinals",

author = "Shimon Garti and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

doi = "10.1007/s10998-025-00628-2",

language = "אנגלית",

journal = "Periodica Mathematica Hungarica",

issn = "0031-5303",

publisher = "Akademiai Kiado",

}

TY - JOUR

T1 - Superclub, splitting, separating statements

AU - Garti, Shimon

AU - Shelah, Saharon

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025

Y1 - 2025

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.

KW - Splitting number

KW - Superclub

KW - The Galvin property

KW - Tiltan

KW - Weakly compact cardinals

UR - http://www.scopus.com/inward/record.url?scp=85218166020&partnerID=8YFLogxK

U2 - 10.1007/s10998-025-00628-2

DO - 10.1007/s10998-025-00628-2

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85218166020

SN - 0031-5303

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

ER -

Superclub, splitting, separating statements

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this