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FORCING CONSTRUCTIONS AND COUNTABLE BOREL EQUIVALENCE RELATIONS

Part of: Set theory Connections with other structures, applications Topological dynamics

Published online by Cambridge University Press:  14 March 2022

SU GAO ,
STEVE JACKSON ,
EDWARD KROHNE  and
BRANDON SEWARD
SU GAO
Affiliation:
SCHOOL OF MATHEMATICAL SCIENCES AND LPMC NANKAI UNIVERSITYTIANJIN300071P.R. CHINAE-mail:sgao@nankai.edu.cn
STEVE JACKSON
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NORTH TEXAS 1155 UNION CIRCLE #311430 DENTON, TX76203, USAE-mail:jackson@unt.eduE-mail:krohneew@gmail.com
EDWARD KROHNE
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NORTH TEXAS 1155 UNION CIRCLE #311430 DENTON, TX76203, USAE-mail:jackson@unt.eduE-mail:krohneew@gmail.com
BRANDON SEWARD
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA SAN DIEGO 9500 GILMAN DRIVE #0112 LA JOLLA, CA92903-0112, USAE-mail:bseward@ucsd.edu
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Abstract

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply the nonexistence of Borel complete sections with certain features.

Keywords

Borel equivalence relationcomplete sectionorbit forcing

MSC classification

Primary: 03E15: Descriptive set theory
Secondary: 03E40: Other aspects of forcing and Boolean-valued models 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 37B20: Notions of recurrence
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 3 , September 2022 , pp. 873 - 893
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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