On the concept of $\boldsymbol {Pi}_1^1$-completeness
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- by Alexander S. Kechris
- Proc. Amer. Math. Soc. 125 (1997), 1811-1814
- DOI: https://doi.org/10.1090/S0002-9939-97-03770-2
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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
- Leo A. Harrington and Alexander S. Kechris, On the determinacy of games on ordinals, Ann. Math. Logic 20 (1981), no. 2, 109–154. MR 622782, DOI 10.1016/0003-4843(81)90001-2
- A. S. Kechris, Classical Descriptive Set Theory, Graduate Texts in Math., vol. 156, Springer-Verlag, 1995.
Bibliographic 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