On $\Game \mathbf {\Gamma }$-complete sets
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- by Gabriel Debs and Jean Saint Raymond PDF
- Proc. Amer. Math. Soc. 148 (2020), 859-873 Request permission
Abstract:
Extending a result of A. Kechris we prove that under suitable assumptions on the class $\mathbf {\Gamma }$ of Borel sets, in particular when $\mathbf {\Gamma }$ is a Baire class, if any $\Game \mathbf {\Gamma }$ set is reducible to some $\Game \mathbf {\Gamma }$ set $A$ by a $\Game \mathbf {\Gamma }$-measurable function, then $A$ is $\Game \mathbf {\Gamma }$-complete.References
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Additional Information
- Gabriel Debs
- Affiliation: Sorbonne Université, Université Paris Diderot, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, F-75005, Paris, France – and – Université Le Havre Normandie, Institut Universitaire de Technologie, Rue Boris Vian, BP 4006 76610 Le Havre, France
- MR Author ID: 55795
- Email: gabriel.debs@imj-prg.fr
- Jean Saint Raymond
- Affiliation: Sorbonne Université, Université Paris Diderot, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, F-75005, Paris, France
- MR Author ID: 153115
- Email: jean.saint-raymond@imj-prg.fr
- Received by editor(s): October 8, 2018
- Received by editor(s) in revised form: May 29, 2019
- Published electronically: August 7, 2019
- Communicated by: Heike Mildenberger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 859-873
- MSC (2010): Primary 03E15, 28A05; Secondary 54H05
- DOI: https://doi.org/10.1090/proc/14731
- MathSciNet review: 4052221