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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the concept of $\boldsymbol {\Pi }^1_1$-completeness


Author: Alexander S. Kechris
Journal: Proc. Amer. Math. Soc. 125 (1997), 1811-1814
MSC (1991): Primary 03E15, 04A15, 28A05, 54H05
MathSciNet review: 1372034
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Abstract: It is shown that two natural notions of completeness for co-analytic sets in Polish spaces, one in terms of continuous reductions and the other in terms of Borel reductions, coincide. The proof uses methods of effective descriptive set theory.


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Additional Information

Alexander S. Kechris
Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Email: kechris@math.caltech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03770-2
PII: S 0002-9939(97)03770-2
Received by editor(s): October 2, 1995
Received by editor(s) in revised form: January 15, 1996
Additional Notes: The author’s research was partially supported by NSF Grant DMS-9317509.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society