On the concept of analytic hardness
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- by Janusz Pawlikowski PDF
- Proc. Amer. Math. Soc. 143 (2015), 1745-1747 Request permission
Abstract:
Let $H\subseteq Z\subseteq 2^{\omega }$. Using only classical descriptive set theory we prove that if Borel functions from $2^{\omega }$ to $Z$ give as preimages of $H$ all analytic subsets of $2^{\omega }$, then so do continuous injections. This strengthens a theorem Kechris proved by means of effective descriptive set theory.References
- Alexander S. Kechris, On the concept of $\bfPi ^1_1$-completeness, Proc. Amer. Math. Soc. 125 (1997), no. 6, 1811–1814. MR 1372034, DOI 10.1090/S0002-9939-97-03770-2
- Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
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
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3314086