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A GAME CHARACTERIZING BAIRE CLASS 1 FUNCTIONS

Published online by Cambridge University Press:  06 June 2019

VIKTOR KISS
VIKTOR KISS*
Affiliation:
ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS HUNGARIAN ACADEMY OF SCIENCES P.O. BOX 127, H-1364 BUDAPEST, HUNGARY and DEPARTMENT OF MATHEMATICS CORNELL UNIVERSITY ITHACA, NY 14853, USAE-mail: [email protected]
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Abstract

Duparc introduced a two-player game for a function f between zero-dimensional Polish spaces in which Player II has a winning strategy iff f is of Baire class 1. We generalize this result by defining a game for an arbitrary function f : X → Y between arbitrary Polish spaces such that Player II has a winning strategy in this game iff f is of Baire class 1. Using the strategy of Player II, we reprove a result concerning first return recoverable functions.

Keywords

Primary 26A21Secondary 03E1554H05Baire class 1 functionsgamedeterminacyderivativefirst return recoverability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 456 - 466
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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