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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
DOI: https://doi.org/10.1090/S0002-9939-97-03770-2
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.


References [Enhancements On Off] (What's this?)

  • 1. L. Harrington and A. S. Kechris, On the determinacy of games on ordinals, Ann. Math. Logic 20 (1981), 109-154. MR 83c:03044
  • 2. A. S. Kechris, Classical Descriptive Set Theory, Graduate Texts in Math., vol. 156, Springer-Verlag, 1995.

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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: https://doi.org/10.1090/S0002-9939-97-03770-2
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

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