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We study the classes of Büchi and Rabin automatic structures. For Büchi (Rabin) automatic structures their domains consist of infinite strings (trees), and the basic relations, including the equality relation, and graphs of operations are recognized by Büchi (Rabin) automata. A Büchi (Rabin) automatic structure is injective if different infinite strings(More)
We announce two new dichotomy theorems for Borel equivalence relations , and present the results in context by giving an overview of related recent developments. space and E a Borel equivalence relation on X , a (complete) classification of X up to E-equivalence consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c(x) = c(y). To be(More)