The Determined Property of Baire in Reverse Math

Eric P. Astor; Damir Dzhafarov; Antonio Montalbán; Reed Solomon; Linda Brown Westrick

doi:10.1017/jsl.2019.64

The Determined Property of Baire in Reverse Math

Eric P. Astor
, Damir Dzhafarov
, Antonio Montalbán
, Reed Solomon
, Linda Brown Westrick

Mathematics

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

2 Scopus citations

Abstract

We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle CD-PB, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than. Any ω-model of must be closed under hyperarithmetic reduction, but is not a theory of hyperarithmetic analysis. We show that whenever is the second-order part of an ω-model of CD-PB, then for every Z M, there is a G M such that G is Δ-generic relative to Z.

Original language	English (US)
Pages (from-to)	166-198
Number of pages	33
Journal	Journal of Symbolic Logic
Volume	85
Issue number	1
DOIs	https://doi.org/10.1017/jsl.2019.64
State	Published - Mar 1 2020

All Science Journal Classification (ASJC) codes

Philosophy
Logic

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10.1017/jsl.2019.64

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title = "The Determined Property of Baire in Reverse Math",

abstract = "We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle CD-PB, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than. Any ω-model of must be closed under hyperarithmetic reduction, but is not a theory of hyperarithmetic analysis. We show that whenever is the second-order part of an ω-model of CD-PB, then for every Z M, there is a G M such that G is Δ-generic relative to Z.",

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AU - Montalbán, Antonio

AU - Solomon, Reed

AU - Westrick, Linda Brown

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AB - We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle CD-PB, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than. Any ω-model of must be closed under hyperarithmetic reduction, but is not a theory of hyperarithmetic analysis. We show that whenever is the second-order part of an ω-model of CD-PB, then for every Z M, there is a G M such that G is Δ-generic relative to Z.

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The Determined Property of Baire in Reverse Math

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