Cardinal characteristics of the continuum and partitions

William Chen; Shimon Garti; Thilo Weinert

doi:https://doi.org/10.1007/s11856-019-1942-y

Cardinal characteristics of the continuum and partitions

William Chen, Shimon Garti, Thilo Weinert

Ben-Gurion University of the Negev, The Hebrew University of Jerusalem

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

Abstract

We prove that for regular cardinals κ, combinations of the stick principle at κ and certain cardinal characteristics at κ being κ⁺ cause partition relations such as κ⁺ → (κ⁺, (κ : 2))² and (κ⁺)² → (κ⁺κ, 4)² to fail. Polarised partition relations are also considered, and the results are used to answer several problems posed by Garti, Larson and Shelah.

Original language	American English
Pages (from-to)	13-38
Number of pages	26
Journal	Israel Journal of Mathematics
Volume	235
Issue number	1
DOIs	https://doi.org/10.1007/s11856-019-1942-y
State	Published - 1 Jan 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1007/s11856-019-1942-y

Cite this

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abstract = "We prove that for regular cardinals κ, combinations of the stick principle at κ and certain cardinal characteristics at κ being κ+ cause partition relations such as κ+ → (κ+, (κ : 2))2 and (κ+)2 → (κ+κ, 4)2 to fail. Polarised partition relations are also considered, and the results are used to answer several problems posed by Garti, Larson and Shelah.",

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AB - We prove that for regular cardinals κ, combinations of the stick principle at κ and certain cardinal characteristics at κ being κ+ cause partition relations such as κ+ → (κ+, (κ : 2))2 and (κ+)2 → (κ+κ, 4)2 to fail. Polarised partition relations are also considered, and the results are used to answer several problems posed by Garti, Larson and Shelah.

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Cardinal characteristics of the continuum and partitions

Abstract

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