Baire-class $\xi$ colorings: The first three levels
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- by Dominique Lecomte and Miroslav Zeleny PDF
- Trans. Amer. Math. Soc. 366 (2014), 2345-2373 Request permission
Abstract:
The $\mathbb {G}_0$-dichotomy due to Kechris, Solecki and Todorčević characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the $\mathbb {G}_0$-dichotomy for $\mathbf {\Sigma }^0_\xi$-measurable countable colorings when $\xi \leq 3$. A $\mathbf {\Sigma }^0_\xi$-measurable countable coloring gives a covering of the diagonal consisting of countably many $\mathbf {\Sigma }^0_\xi$ squares. This leads to the study of countable unions of $\mathbf {\Sigma }^0_\xi$ rectangles. We also give a Hurewicz-like dichotomy for such countable unions when $\xi \leq 2$.References
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Additional Information
- Dominique Lecomte
- Affiliation: Université de Picardie, I.U.T. de l’Oise, site de Creil, 13, allée de la faïencerie, 60 107 Creil, France
- Address at time of publication: Institut de Mathématiques de Jussieu, Université Paris 6, Projet Analyse Fonctionnelle, Couloir 16-26, 4ème étage, Case 247, 4, place Jussieu, 75 252 Paris Cedex 05, France
- MR Author ID: 336400
- Email: dominique.lecomte@upmc.fr
- Miroslav Zeleny
- Affiliation: Faculty of Mathematics and Physics, Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic
- Email: zeleny@karlin.mff.cuni.cz
- Received by editor(s): April 16, 2011
- Received by editor(s) in revised form: May 11, 2012
- Published electronically: January 28, 2014
- Additional Notes: The work was part of the research project MSM 0021620839 financed by MSMT and partly supported by the grant GAČR 201/09/0067.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 2345-2373
- MSC (2010): Primary 03E15; Secondary 54H05
- DOI: https://doi.org/10.1090/S0002-9947-2014-05876-5
- MathSciNet review: 3165641