Polarized relations at singulars over successors

Shimon Garti

doi:10.1016/j.disc.2020.111961

Polarized relations at singulars over successors

Shimon Garti

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

Erdős, Hajnal and Rado asked whether [Formula presented] and whether [Formula presented]. We shall prove that both relations are independent over ZFC. We shall also prove that [Formula presented] is independent over ZF for some μ>cf(μ)=ω₁.

Original language	English
Article number	111961
Journal	Discrete Mathematics
Volume	343
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2020.111961
State	Published - 1 Sep 2020

Keywords

Determinacy
Generalized Martin's axiom
Polarized partition relations
Scales

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2020.111961

Cite this

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title = "Polarized relations at singulars over successors",

abstract = "Erd{\H o}s, Hajnal and Rado asked whether [Formula presented] and whether [Formula presented]. We shall prove that both relations are independent over ZFC. We shall also prove that [Formula presented] is independent over ZF for some μ>cf(μ)=ω1.",

keywords = "Determinacy, Generalized Martin's axiom, Polarized partition relations, Scales",

author = "Shimon Garti",

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year = "2020",

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doi = "10.1016/j.disc.2020.111961",

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N2 - Erdős, Hajnal and Rado asked whether [Formula presented] and whether [Formula presented]. We shall prove that both relations are independent over ZFC. We shall also prove that [Formula presented] is independent over ZF for some μ>cf(μ)=ω1.

AB - Erdős, Hajnal and Rado asked whether [Formula presented] and whether [Formula presented]. We shall prove that both relations are independent over ZFC. We shall also prove that [Formula presented] is independent over ZF for some μ>cf(μ)=ω1.

KW - Determinacy

KW - Generalized Martin's axiom

KW - Polarized partition relations

KW - Scales

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DO - 10.1016/j.disc.2020.111961

M3 - مقالة

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

M1 - 111961

ER -

Polarized relations at singulars over successors

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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