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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: kiss.viktor@renyi.mta.hu
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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

REFERENCES

Andretta, A., More on Wadge determinacy. Annals of Pure and Applied Logic, vol. 144 (2006), no. 1–3, pp. 2–32.CrossRefGoogle Scholar
Carroy, R., Playing in the first Baire class. Mathematical Logic Quarterly, vol. 60 (2014), no. 1–2, pp. 118–132.CrossRefGoogle Scholar
Darji, U. B. and Evans, M. J., Recovering Baire 1 functions. Mathematika, vol. 42 (1995), no. 1, pp. 43–48.CrossRefGoogle Scholar
Duncan, J. and Solecki, S., Recovering Baire one functions on ultrametric spaces. Bulletin of the London Mathematical Society, vol. 41 (2009), no. 4, pp. 747–756.CrossRefGoogle Scholar
Duparc, J., Wadge hierarchy and Veblen hierarchy. I. Borel sets of finite rank, this Journal, vol. 66 (2001), no. 1, pp. 56–86.Google Scholar
Kechris, A. S., Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995.CrossRefGoogle Scholar
Lecomte, D., How can we recover Baire class one functions? Mathematika, vol. 50 (2003), no. 1–2, pp. 171–198 (2005).CrossRefGoogle Scholar
Ros, L. M., Game representations of classes of piecewise definable functions. Mathematical Logic Quarterly, vol. 57 (2011), no. 1, pp. 95–112.Google Scholar
Nobrega, H., Games for functions of a fixed baire class, preprint.Google Scholar
Semmes, B., Games, trees, and Borel functions, Ph.D. thesis, University of Amsterdam, 2009.Google Scholar
Wadge, W. W., Reducibility and determinateness on the Baire space, ProQuest LLC, Ann Arbor, MI, Ph.D. thesis, University of California, Berkeley, 1983.Google Scholar