Borel And Baire Reducibility

• Main Author: Harvey M. Friedman
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 1999
• Subjects: Dougherty; sami
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.1966; http://www.math.ohio-state.edu/foundations/ps/23-reducibilityequivrelations.ps

INTRODUCTION The Borel reducibility theory of Polish equivalence relations, at least in its present form, was initiated in [FS89]. There is now an extensive literature on this topic, including fundamental work on the Glimm-Effros dichotomy in [HKL90], on countable Borel equivalence relations in [DJK94], and on Polish group actions in [BK96]. Current principal contributors include H. Becker, R. Dougherty, L. Harrington, G. Hjorth, S. Jackson, A.S. Kechris, and A. Louveau, R. Sami, and S. Solecki. A Polish space is a topological space that is separable and completely metrizable. The Borel subsets of a Polish space form the least s-algebra containing the open subsets. A Borel function from one Polish space to another is a function such that the inverse image of every open set is Borel. Two Polish spaces are Borel isomorphic if and only if there is a one-one onto Borel function from the first onto the second. This is an equivalence relation. Any two uncountable Polish sp