Martin's conjecture and strong ergodicity

Simon Thomas

doi:10.1007/s00153-009-0148-0

Martin's conjecture and strong ergodicity

Simon Thomas

School of Arts and Sciences, Mathematics

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

12 Scopus citations

Abstract

In this paper, we explore some of the consequences of Martin's Conjecture on degree invariant Borel maps. These include the strongest conceivable ergodicity result for the Turing equivalence relation with respect to the filter on the degrees generated by the cones, as well as the statement that the complexity of a weakly universal countable Borel equivalence relation always concentrates on a null set.

Original language	English (US)
Pages (from-to)	749-759
Number of pages	11
Journal	Archive for Mathematical Logic
Volume	48
Issue number	8
DOIs	https://doi.org/10.1007/s00153-009-0148-0
State	Published - Nov 2009

All Science Journal Classification (ASJC) codes

Philosophy
Logic

Keywords

Borel equivalence relation
Turing degree

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10.1007/s00153-009-0148-0

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title = "Martin's conjecture and strong ergodicity",

abstract = "In this paper, we explore some of the consequences of Martin's Conjecture on degree invariant Borel maps. These include the strongest conceivable ergodicity result for the Turing equivalence relation with respect to the filter on the degrees generated by the cones, as well as the statement that the complexity of a weakly universal countable Borel equivalence relation always concentrates on a null set.",

keywords = "Borel equivalence relation, Turing degree",

author = "Simon Thomas",

note = "Funding Information: Research partially supported by NSF Grant DMS 0600940.",

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AB - In this paper, we explore some of the consequences of Martin's Conjecture on degree invariant Borel maps. These include the strongest conceivable ergodicity result for the Turing equivalence relation with respect to the filter on the degrees generated by the cones, as well as the statement that the complexity of a weakly universal countable Borel equivalence relation always concentrates on a null set.

KW - Borel equivalence relation

KW - Turing degree

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ER -

Martin's conjecture and strong ergodicity

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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