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THE DETERMINED PROPERTY OF BAIRE IN REVERSE MATH
The Journal of Symbolic Logic ( IF 0.5 ) Pub Date : 2019-09-10 , DOI: 10.1017/jsl.2019.64 ERIC P. ASTOR , DAMIR DZHAFAROV , ANTONIO MONTALBÁN , REED SOLOMON , LINDA BROWN WESTRICK
The Journal of Symbolic Logic ( IF 0.5 ) Pub Date : 2019-09-10 , DOI: 10.1017/jsl.2019.64 ERIC P. ASTOR , DAMIR DZHAFAROV , ANTONIO MONTALBÁN , REED SOLOMON , LINDA BROWN WESTRICK
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 .
中文翻译:
反向数学中 BAIRE 的确定性质
我们在逆向数学中定义了完全确定的Borel码的概念,并考虑了原理$CD-PB$ ,它表明每个完全确定的 Borel 集都具有 Baire 的性质。我们证明了这个原则严格地弱于$AT{R_0}$ . 任何ω -模型$CD-PB$ 必须在超算术减少下关闭,但$CD-PB$ 不是超算术分析的理论。我们表明,无论何时$M \subseteq {2^\omega }$ 是一个的二阶部分ω -模型$CD-PB$ ,那么对于每个$Z \in M$ ,有一个$G \in M$ 这样G 是${\rm{\Delta }}_1^1$ -泛型相对于Z .
更新日期:2019-09-10
中文翻译:
反向数学中 BAIRE 的确定性质
我们在逆向数学中定义了完全确定的Borel码的概念,并考虑了原理