Partition properties of ω1 compatible with CH

Uri Abraham; Stevo Todorčević

Partition properties of ω₁ compatible with CH

Uri Abraham, Stevo Todorčević

Department of Mathematics

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

50 Scopus citations

Abstract

A combinatorial statement concerning ideals of countable subsets of ω₁ is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω₁,ω*₁)-gaps are Hausdorff, and that every coherent sequence on ω₁ either almost includes or is orthogonal to some uncountable subset of ω₁.

Original language	English
Pages (from-to)	165-181
Number of pages	17
Journal	Fundamenta Mathematicae
Volume	152
Issue number	2
State	Published - 1 Jan 1997

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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abstract = "A combinatorial statement concerning ideals of countable subsets of ω1 is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω1,ω*1)-gaps are Hausdorff, and that every coherent sequence on ω1 either almost includes or is orthogonal to some uncountable subset of ω1.",

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AB - A combinatorial statement concerning ideals of countable subsets of ω1 is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω1,ω*1)-gaps are Hausdorff, and that every coherent sequence on ω1 either almost includes or is orthogonal to some uncountable subset of ω1.

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Partition properties of ω₁ compatible with CH

Abstract

ASJC Scopus subject areas

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