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On the concept of analytic hardness


Author: Janusz Pawlikowski
Journal: Proc. Amer. Math. Soc. 143 (2015), 1745-1747
MSC (2010): Primary 03E15, 54H05
DOI: https://doi.org/10.1090/S0002-9939-2014-12422-1
Published electronically: December 19, 2014
MathSciNet review: 3314086
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Abstract: Let $ H\subseteq Z\subseteq \mathit {2}^{\omega }$. Using only classical descriptive set theory we prove that if Borel functions from $ \mathit {2}^{\omega }$ to $ Z$ give as preimages of $ H$ all analytic subsets of $ \mathit {2}^{\omega }$, then so do continuous injections. This strengthens a theorem Kechris proved by means of effective descriptive set theory.


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Additional Information

Janusz Pawlikowski
Affiliation: Department of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email: Janusz.Pawlikowski@math.uni.wroc.pl

DOI: https://doi.org/10.1090/S0002-9939-2014-12422-1
Received by editor(s): June 4, 2013
Published electronically: December 19, 2014
Additional Notes: The author was supported by grant N N201 418939 of the MNiSW (Ministry of Science and Higher Education)
Communicated by: Mirna Dzamonja
Article copyright: © Copyright 2014 American Mathematical Society