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

Research output: Contribution to journalArticle

  • Chris Le Sueur
Original languageEnglish
Pages (from-to)83-115
Number of pages33
JournalAnnals of Pure and Applied Logic
Issue number1
DateAccepted/In press - 11 Aug 2017
DatePublished (current) - 1 Jan 2018


In this paper we develop a technique for proving determinacy of classes of the form ω21 1+Γ (a refinement of the difference hierarchy on Π1 1 lying between ω21 1 and (ω2+1)-Π1 1) from weak principles, establishing upper bounds for the determinacy-strength of the classes ω21 1α 0 for all computable α and of ω21 11 1. This bridges the gap between previously known hypotheses implying determinacy in this region.

    Research areas

  • Descriptive set theory, Determinacy


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