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

Chris Le Sueur

doi:10.1016/j.apal.2017.10.001

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

Chris Le Sueur

School of Mathematics

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Abstract

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 language	English
Pages (from-to)	83-115
Journal	Annals of Pure and Applied Logic
Volume	169
Issue number	1
Early online date	17 Oct 2017
DOIs	https://doi.org/10.1016/j.apal.2017.10.001
Publication status	Published - Jan 2018

Keywords

Determinacy
Descriptive Set Theory

Access to Document

10.1016/j.apal.2017.10.001Licence: Unspecified

Accepted manuscriptAccepted author manuscript, 410 KBLicence: CC BY-NC-ND

https://arxiv.org/abs/1411.1106Licence: CC BY-NC-ND

Cite this

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AB - 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.

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KW - Descriptive Set Theory

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DO - 10.1016/j.apal.2017.10.001

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