Homogeneous Borel sets

van Engelen, Fons

doi:10.1090/S0002-9939-1986-0826501-2

Homogeneous Borel sets
HTML articles powered by AMS MathViewer

by Fons van Engelen PDF

Proc. Amer. Math. Soc. 96 (1986), 673-682 Request permission

Abstract:

Topological characterizations of all zero-dimensional homogeneous absolute Borel sets are obtained; it turns out that there are ${\omega _1}$ such spaces. We use results from game theory—particularly, about Wadge classes.

References

Fons van Engelen, Homogeneous Borel sets of ambiguous class two, Trans. Amer. Math. Soc. 290 (1985), no. 1, 1–39. MR 787953, DOI 10.1090/S0002-9947-1985-0787953-3
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779

Topologie

Contribution à la théorie des ensembles homéomorphes

6

A. Louveau, Some results in the Wadge hierarchy of Borel sets, Cabal seminar 79–81, Lecture Notes in Math., vol. 1019, Springer, Berlin, 1983, pp. 28–55. MR 730585, DOI 10.1007/BFb0071692
Jan van Mill, Characterization of some zero-dimensional separable metric spaces, Trans. Amer. Math. Soc. 264 (1981), no. 1, 205–215. MR 597877, DOI 10.1090/S0002-9947-1981-0597877-9
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 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
Robert Van Wesep, Wadge degrees and descriptive set theory, Cabal Seminar 76–77 (Proc. Caltech-UCLA Logic Sem., 1976–77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp. 151–170. MR 526917

Degrees of complexity of subsets of the Baire space

19