Description
Book SynopsisThe theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, combinatorics, functional analysis, and model theory. The book presents major aspects of this theory and its applications.
Table of ContentsIntroduction Descriptive set theoretic background Some theorems of descriptive set theory Borel ideals Introduction to equivalence relations Borel reducibility of equivalence relations "Elementary" results Introduction to countable equivalence relations Hyperfinite equivalence relations More on countable equivalence relations The 1st and 2nd dichotomy theorems Ideal ${\mathscr I}_1$ and the equivalence relation ${\mathsf E}_1$ Actions of the infinite symmetric group Turbulent groups actions The ideal $\mathscr{I}_3$ and the equivalence relation $\mathsf{E}_3$ Summable equivalence relations $\mathsf{c}_0$-equalities Pinned equivalence relations Reduction of Borel equivalence relations to Borel ideals On Cohen and Gandy-Harrington forcing over countable models Bibliography Index.
