A Gδ ideal of compact sets strictly above the nowhere dense ideal in the Tukey order

Justin Tatch Moore; Sławomir Solecki

doi:10.1016/j.apal.2008.07.003

A G_δ ideal of compact sets strictly above the nowhere dense ideal in the Tukey order

Justin Tatch Moore, Sławomir Solecki

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

Abstract

We prove that there is a G_δ σ-ideal of compact sets which is strictly above NWD in the Tukey order. Here NWD is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 (1-3) (1999) 171-195].

Original language	English (US)
Pages (from-to)	270-273
Number of pages	4
Journal	Annals of Pure and Applied Logic
Volume	156
Issue number	2-3
DOIs	https://doi.org/10.1016/j.apal.2008.07.003
State	Published - Dec 2008
Externally published	Yes

Keywords

Ideal of compact sets
Tukey reduction

ASJC Scopus subject areas

Logic

Online availability

10.1016/j.apal.2008.07.003

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Cite this

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title = "A Gδ ideal of compact sets strictly above the nowhere dense ideal in the Tukey order",

abstract = "We prove that there is a Gδ σ-ideal of compact sets which is strictly above NWD in the Tukey order. Here NWD is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veli{\v c}kovi{\'c} asked in [Alain Louveau, Boban Veli{\v c}kovi{\'c}, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 (1-3) (1999) 171-195].",

keywords = "Ideal of compact sets, Tukey reduction",

author = "Moore, {Justin Tatch} and S{\l}awomir Solecki",

note = "Funding Information: The second author acknowledges the support of NSF grant DMS–0700841.",

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AU - Solecki, Sławomir

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PY - 2008/12

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N2 - We prove that there is a Gδ σ-ideal of compact sets which is strictly above NWD in the Tukey order. Here NWD is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 (1-3) (1999) 171-195].

AB - We prove that there is a Gδ σ-ideal of compact sets which is strictly above NWD in the Tukey order. Here NWD is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 (1-3) (1999) 171-195].

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KW - Tukey reduction

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