A note on an effective Polish topology and Silver’s dichotomy theorem
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- by Ramez L. Sami PDF
- Proc. Amer. Math. Soc. 147 (2019), 4039-4044 Request permission
Abstract:
$\boldsymbol {\cdot }$ We define a Polish topology inspired from the Gandy-Harrington topology and show how it can be used to prove Silver’s dichotomy theorem while remaining in the Polish realm.
$\boldsymbol {\cdot }$ In this topology, a $\Pi _{1}^{1}$ equivalence decomposes into a “sum” of a clopen relation and a meager one.
$\boldsymbol {\cdot }$ We characterize it as the largest regular topology with a basis included in $\Sigma _{1}^{1}$.
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Additional Information
- Ramez L. Sami
- Affiliation: Department of Mathematics, Université Paris-Diderot, 75205 Paris, Cedex 13, France
- MR Author ID: 153835
- Email: sami@univ-paris-diderot.fr
- Received by editor(s): January 6, 2019
- Published electronically: June 14, 2019
- Communicated by: Heike Mildenberger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4039-4044
- MSC (2010): Primary 03E15; Secondary 28A05, 54H05
- DOI: https://doi.org/10.1090/proc/14541
- MathSciNet review: 3993795