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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the concept of $\boldsymbol {Pi}_1^1$-completeness
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by Alexander S. Kechris PDF
Proc. Amer. Math. Soc. 125 (1997), 1811-1814 Request permission

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
  • MR Author ID: 99660
  • Email: kechris@math.caltech.edu
  • 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
  • © Copyright 1997 American Mathematical Society
  • 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