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Decomposing Baire functions

Published online by Cambridge University Press:  12 March 2014

J. Cichoń ,
M. Morayne ,
J. Pawlikowski  and
S. Solecki
J. Cichoń
Affiliation:
Mathematical Institute, University of Wroclaw, 50–384 Wrocław, Poland
M. Morayne
Affiliation:
Mathematical Institute, University of Wroclaw, 50–384 Wrocław, Poland
J. Pawlikowski
Affiliation:
Mathematical Institute, University of Wroclaw, 50–384 Wrocław, Poland
S. Solecki*
Affiliation:
Mathematical Institute, University of Wroclaw, 50–384 Wrocław, Poland
*
Department of Mathematics, University of California, Davis, California 95616-8633.
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Abstract

We discuss in the paper the following problem: Given a function in a given Baire class, into “how many” (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.

Keywords

Baire functionBaire classBorel setcardinal numberBaire space
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1273 - 1283
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

[BS]Blass, A. and Shelah, S., Ultrafilters with small generating sets, Israel Journal of Mathematics, vol. 65 (1989), pp. 259–271.CrossRefGoogle Scholar
[CM]Cichoń, J. and Morayne, M., Universal functions and generalized classes of functions, Proceedings of the American Mathematical Society, vol. 102 (1988), pp. 83–89.CrossRefGoogle Scholar
[JR]Jayne, J. E. and Rogers, C. A., First level Borel functions and isomorphisms, Journal de Mathematiques Pures et Appliquées, ser. 9, vol. 61 (1982), pp. 177–205.Google Scholar
[K]Kuratowski, K., Topology, Vol. 1, 5th ed., PWN, Warsaw, and Academic Press, New York, 1966.Google Scholar
[L]Lindenbaum, A., Sur les superpositions de fonctions representables analytiquement, Fundamenta Mathematicae, vol. 23 (1934), pp. 15–37.CrossRefGoogle Scholar
[M]Moschovakis, Y. N., Descriptive set theory, North-Holland, Amsterdam, 1980.Google Scholar
[O]Oxtoby, J. C., Measure and category, Springer-Verlag, Berlin, 1971.CrossRefGoogle Scholar