The determined property of Baire in reverse math
The Journal of Symbolic Logic, 2020•cambridge.org
… 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 ATR0. Any -model of
CD-PB must be closed under hyperarithmetic reduction, but CD-PB is not a theory of
hyperarithmetic analysis. … Here we propose another definition for a Borel set in reverse
mathematics, distinguished from the original by the terminology completely determined …
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 ATR0. Any -model of
CD-PB must be closed under hyperarithmetic reduction, but CD-PB is not a theory of
hyperarithmetic analysis. … Here we propose another definition for a Borel set in reverse
mathematics, distinguished from the original by the terminology completely determined …
We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle -generic relative to Z.
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