Uniformisations partielles et critères à la Hurewicz dans le plan
HTML articles powered by AMS MathViewer
- by Dominique Lecomte PDF
- Trans. Amer. Math. Soc. 347 (1995), 4433-4460 Request permission
Abstract:
Résumé: On donne des caractérisations des boréliens potentiellement d’une classe de Wadge donnée, parmi les boréliens à coupes verticales dénombrables d’un produit de deux espaces polonais. Pour ce faire, on utilise des résultats d’uniformisation partielle.References
- Gabriel Debs and Jean Saint-Raymond, Sélections boréliennes injectives, Amer. J. Math. 111 (1989), no. 3, 519–534 (French). MR 1002011, DOI 10.2307/2374671
- Siegfried Graf and R. Daniel Mauldin, Measurable one-to-one selections and transition kernels, Amer. J. Math. 107 (1985), no. 2, 407–425. MR 784290, DOI 10.2307/2374421
- L. A. Harrington, A. S. Kechris, and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), no. 4, 903–928. MR 1057041, DOI 10.1090/S0894-0347-1990-1057041-5
- Alexander S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337–384. MR 369072, DOI 10.1016/0003-4843(73)90012-0
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- Dominique Lecomte, Classes de Wadge potentielles et théorèmes d’uniformisation partielle, Fund. Math. 143 (1993), no. 3, 231–258 (French, with French summary). MR 1247803, DOI 10.4064/fm-143-3-231-258
- Dominique Lecomte, Classes de Wadge potentielles des boréliens à coupes dénombrables, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 11, 1045–1048 (French, with English and French summaries). MR 1249786 A. Louveau, Livre à paraître. —, Ensembles analytiques et boréliens dans les espaces produit, Astérisque (S. M. F.) 78 (1980).
- A. Louveau and J. Saint-Raymond, Borel classes and closed games: Wadge-type and Hurewicz-type results, Trans. Amer. Math. Soc. 304 (1987), no. 2, 431–467. MR 911079, DOI 10.1090/S0002-9947-1987-0911079-0
- R. Daniel Mauldin, One-to-one selections—marriage theorems, Amer. J. Math. 104 (1982), no. 4, 823–828. MR 667537, DOI 10.2307/2374207
- Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443, DOI 10.1007/978-1-4684-9339-9
- John R. Steel, Analytic sets and Borel isomorphisms, Fund. Math. 108 (1980), no. 2, 83–88. MR 594307, DOI 10.4064/fm-108-2-83-88
- Jean Saint-Raymond, La structure borélienne d’Effros est-elle standard?, Fund. Math. 100 (1978), no. 3, 201–210 (French). MR 509546, DOI 10.4064/fm-100-3-201-210 W. W. Wadge, Thesis, Berkeley, 1984.
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 4433-4460
- MSC: Primary 03E15; Secondary 28A05, 54H05
- DOI: https://doi.org/10.1090/S0002-9947-1995-1316855-5
- MathSciNet review: 1316855