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ASYMMETRIC CUT AND CHOOSE GAMES

Part of: Set theory

Published online by Cambridge University Press:  28 July 2023

CHRISTOPHER HENNEY-TURNER Open the ORCID record for CHRISTOPHER HENNEY-TURNER [Opens in a new window] ,
PETER HOLY Open the ORCID record for PETER HOLY [Opens in a new window] ,
PHILIPP SCHLICHT Open the ORCID record for PHILIPP SCHLICHT [Opens in a new window]  and
PHILIP WELCH Open the ORCID record for PHILIP WELCH [Opens in a new window]
CHRISTOPHER HENNEY-TURNER
Affiliation:
INSTITUTE OF MATHEMATICS OF THE POLISH ACADEMY OF SCIENCES ANTONIEGO ABRAHAMA 18 81-825 SOPOT POLAND E-mail: cturner@impan.pl
PETER HOLY
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TECHNISCHE UNIVERSITÄT WIEN WIEDNER HAUPTSTRAßE 8–10/104 1040 WIEN AUSTRIA E-mail: pholy@math.uni-bonn.de
PHILIPP SCHLICHT
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF BRISTOL FRY BUILDING, WOODLAND ROAD BRISTOL BS8 1UG UK E-mail: philipp.schlicht@bristol.ac.uk
PHILIP WELCH
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF BRISTOL FRY BUILDING, WOODLAND ROAD BRISTOL BS8 1UG UK E-mail: p.welch@bristol.ac.uk
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Abstract

We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity, strategic closure, and precipitousness.

Keywords

cut and choose gamesgenerically measurable cardinalsdistributivityBanach-Mazur gamesprecipitous ideals

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 03E55: Large cardinals 03E35: Consistency and independence results
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 29 , Issue 4 , December 2023 , pp. 588 - 625
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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