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arXiv · 1411.1106

Determinacy of Refinements to the Difference Hierarchy of Co-analytic Sets

Chris Le Sueur
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Abstract

In this paper we develop a technique for proving determinacy of classes of the form $ω^2-Π^1_1+Γ$ (a refinement of the difference hierarchy on the co-analytic sets lying between $ω^2-Π^1_1$ and $(ω^2+1)-Π^1_1$) from weak principles, establishing upper bounds for the determinacy-strength of the classes $ω^2-Π^1_1+Σ^0_α$ for all computable $α$ and of $ω^2-Π^1_1+Δ^1_1$. This bridges the gap between previously known hypotheses implying determinacy in this region.

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Chris Le Sueur. 2017-10-23. Determinacy of Refinements to the Difference Hierarchy of Co-analytic Sets. https://doi.org/10.1016/j.apal.2017.10.001

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