Determinacy of refinements to the difference hierarchy of co-analytic sets

Chris Le Sueur

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In this paper we develop a technique for proving determinacy of classes of the form ω²-Π¹₁+Γ (a refinement of the difference hierarchy on Π¹₁ lying between ω²-Π¹₁ and (ω²+1)-Π¹₁) from weak principles, establishing upper bounds for the determinacy- strength of the classes ω²-Π¹₁+Σ^0_α for all computable α and of ω²-Π¹₁+Δ¹₁. This bridges the gap between previously known hypotheses implying determinacy in this region.
Original languageEnglish
Pages (from-to)83-115
Number of pages33
JournalAnnals of Pure and Applied Logic
Issue number1
Early online date17 Oct 2017
Publication statusPublished - Jan 2018


  • Determinacy
  • Descriptive Set Theory

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