Determinacy in the difference hierarchy of co-analytic sets
type: Item
instance of: scholarly article
title: Determinacy in the difference hierarchy of co-analytic sets
zbMATH Open document ID: 0856.03041
DOI: 10.1016/0168-0072(95)00057-7
author: Yanyan Li
published in: Annals of Pure and Applied Logic
publication date: 1997-02-24T00:00:00Z
review text: It is shown for recursive ordinals \(\alpha\) that \(\omega^2\alpha- \Pi^1_1\) determinacy is equivalent to existence of a clever \(\alpha\)-mouse. It is also shown for every countable ordinal \(\delta\) that if there is a sequence \(\langle \kappa_i: i< \delta+ 1\rangle\) of measurable cardinals and an almost \(< \omega_1\)-Erdös cardinal above them, then \(\omega^2(\delta+ 1)- \Pi^1_1\) determinacy holds. It is also shown that if the Weak Chang Conjecture holds at \(\omega_1\), then \(\omega^2- \Pi^1_1\) determinacy holds.
Mathematics Subject Classification ID: 03E60
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 908481
zbMATH Keywords: difference hierarchy
zbMATH Keywords: coanalytic sets
zbMATH Keywords: indiscernibles
zbMATH Keywords: mouse
zbMATH Keywords: core model
zbMATH Keywords: Erdös cardinal
zbMATH Keywords: determinacy
zbMATH Keywords: measurable cardinals
zbMATH Keywords: Weak Chang Conjecture
MaRDI profile type: Publication
full work available at URL: 0168-0072(95)00057-7
OpenAlex ID: W2083499924
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description: scientific article; zbMATH DE number 908481