Equivalence relations and determinacy

Logan Crone; Lior Fishman; Stephen Jackson

doi:10.1142/S0219061322500039

Equivalence relations and determinacy

Logan Crone
, Lior Fishman
, Stephen Jackson

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce the notion of (F,E)-determinacy for F a pointclass and E an equivalence relation on a Polish space X. A case of particular interest is the case when E = EG is the (left) shift-action of G on SG where S = 2 = {0, 1} or S = ω. We show that for all shift actions by countable groups G, and any "reasonable"pointclass F, that (F,EG)-determinacy implies F-determinacy. We also prove a corresponding result when E is a subshift of finite type of the shift map on 2ℤ.

Original language	English
Article number	2250003
Journal	Journal of Mathematical Logic
Volume	22
Issue number	1
DOIs	https://doi.org/10.1142/S0219061322500039
State	Published - 1 Apr 2022
Externally published	Yes

Keywords

Descriptive set theory
determinacy
equivalence relations
games

ASJC Scopus subject areas

Logic

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10.1142/S0219061322500039

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AU - Jackson, Stephen

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AB - We introduce the notion of (F,E)-determinacy for F a pointclass and E an equivalence relation on a Polish space X. A case of particular interest is the case when E = EG is the (left) shift-action of G on SG where S = 2 = {0, 1} or S = ω. We show that for all shift actions by countable groups G, and any "reasonable"pointclass F, that (F,EG)-determinacy implies F-determinacy. We also prove a corresponding result when E is a subshift of finite type of the shift map on 2ℤ.

KW - Descriptive set theory

KW - determinacy

KW - equivalence relations

KW - games

UR - https://www.scopus.com/pages/publications/85124719425

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DO - 10.1142/S0219061322500039

M3 - Article

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VL - 22

JO - Journal of Mathematical Logic

JF - Journal of Mathematical Logic

IS - 1

M1 - 2250003

ER -

Equivalence relations and determinacy

Abstract

Keywords

ASJC Scopus subject areas

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