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- Title
THE DETERMINED PROPERTY OF BAIRE IN REVERSE MATH.
- Authors
ASTOR, ERIC P.; DZHAFAROV, DAMIR; MONTALBÁN, ANTONIO; SOLOMON, REED; WESTRICK, LINDA BROWN
- 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 $AT{R_0}$. Any ω -model of $CD - PB$ must be closed under hyperarithmetic reduction, but $CD - PB$ is not a theory of hyperarithmetic analysis. We show that whenever $M \subseteq {2^\omega }$ is the second-order part of an ω -model of $CD - PB$ , then for every $Z \in M$ , there is a $G \in M$ such that G is ${\rm{\Delta }}_1^1$ -generic relative to Z.
- Subjects
DELTA State (Nigeria); BOREL sets; REVERSE mathematics; MATHEMATICS
- Publication
Journal of Symbolic Logic, 2020, Vol 85, Issue 1, p166
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2019.64