2021/07/22 by Yinhe Peng, Peng, Yinhe, Liuzhen Wu +3
Computer Science · Mathematics · #03D28 #03E05 #03E15 #03E25 #03E60 #28A80 #68Q30 #Algorithms and Data Compression #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2107.10470
openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Strongly Turing determinacy, or sTD, says that for any set A of reals, if ∀ x∃ y≥T x (y∈ A), then there is a pointed set P⊆ A. We prove the following consequences of Turing determinacy (TD) and sTD: (1). ZF+TD implies weakly dependent choice (wDC). (2). ZF+sTD implies that every set of reals is measurable and has Baire property. (3). ZF+sTD implies that every uncountable set of reals has a perfect subset. (4). ZF+sTD implies that for any set of reals A and any ε>0, (a) there is a closed set F⊆ A so that DimH(F)≥ DimH(A)-ε. (b) there is a closed set F⊆ A so that DimP(F)≥ DimP(A)-ε.