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

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

In this paper we develop a technique for proving determinacy of classes of the form ω²-Π₁ ¹+Γ (a refinement of the difference hierarchy on Π₁ ¹ lying between ω²-Π₁ ¹ and (ω²+1)-Π₁ ¹) from weak principles, establishing upper bounds for the determinacy-strength of the classes ω²-Π₁ ¹+Σ_α ⁰ for all computable α and of ω²-Π₁ ¹+Δ¹ ₁. This bridges the gap between previously known hypotheses implying determinacy in this region.

Original language	English
Pages (from-to)	83-115
Number of pages	33
Journal	Annals of Pure and Applied Logic
Volume	169
Issue number	1
DOIs	https://doi.org/10.1016/j.apal.2017.10.001
Publication status	Published - 1 Jan 2018

Keywords

Descriptive set theory
Determinacy

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AB - In this paper we develop a technique for proving determinacy of classes of the form ω2-Π1 1+Γ (a refinement of the difference hierarchy on Π1 1 lying between ω2-Π1 1 and (ω2+1)-Π1 1) from weak principles, establishing upper bounds for the determinacy-strength of the classes ω2-Π1 1+Σα 0 for all computable α and of ω2-Π1 1+Δ1 1. This bridges the gap between previously known hypotheses implying determinacy in this region.

KW - Descriptive set theory

KW - Determinacy

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M3 - Article (Academic Journal)

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 1

ER -

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

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