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BASES FOR FUNCTIONS BEYOND THE FIRST BAIRE CLASS

Part of: Classical measure theory Connections with other structures, applications Real functions Set theory

Published online by Cambridge University Press:  27 October 2020

RAPHAËL CARROY  and
BENJAMIN D. MILLER
RAPHAËL CARROY
Affiliation:
DIPARTIMENTO DI MATEMATICA “GIUSEPPE PEANO” UNIVERSITÀ DI TORINO PALAZZO CAMPANA, VIA CARLO ALBERTO 10 10123TORINO, ITALIAE-mail: raphael.carroy@unito.itURL: http://www.logique.jussieu.fr/~carroy/indexeng.html
BENJAMIN D. MILLER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF VIENNA OSKAR MORGENSTERN PLATZ 11090WIEN, AUSTRIAE-mail: benjamin.miller@univie.ac.atURL: https://homepage.univie.ac.at/benjamin.miller/
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Abstract

We provide a finite basis for the class of Borel functions that are not in the first Baire class, as well as the class of Borel functions that are not $\sigma $ -continuous with closed witnesses.

Keywords

Baire classbasisembeddingsigma-continuous

MSC classification

Primary: 03E15: Descriptive set theory
Secondary: 26A21: Classification of real functions; Baire classification of sets and functions 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 1289 - 1303
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Copyright
© The Association for Symbolic Logic 2020

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References

REFERENCES

Carroy, R., Miller, B. D., and Soukup, D. T., The open dihypergraph dichotomy and the second level of the Borel hierarchy , Trends in Set Theory (Coskey, S. and Sargsyan, G., editors), Contemporary Mathematics, vol. 752, American Mathematical Society, Providence, RI, 2020, pp. 1–19.CrossRefGoogle Scholar
Jayne, J. E. and Rogers, C. A., First level Borel functions and isomorphisms . Journal de Mathématiques Pures et Appliquées , vol. 61(1982), no. 2, pp. 177–205.Google Scholar
Kechris, A. S., Classical Descriptive Set Theory , Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, NY, 1995.CrossRefGoogle Scholar
Solecki, S., Decomposing Borel sets and functions and the structure of Baire class $1$ functions . Journal of the American Mathematical Society , vol. 11(1998), no. 3, pp. 521–550.CrossRefGoogle Scholar