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BASES FOR FUNCTIONS BEYOND THE FIRST BAIRE CLASS

Part of: Classical measure theory Real functions Connections with other structures, applications 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 10123 TORINO, ITALIA E-mail: raphael.carroy@unito.it URL: http://www.logique.jussieu.fr/~carroy/indexeng.html
BENJAMIN D. MILLER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF VIENNA OSKAR MORGENSTERN PLATZ 1 1090 WIEN, AUSTRIA E-mail: benjamin.miller@univie.ac.at URL: 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)

Information

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

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