# Classical Proofs of Silver’s Theorem and the Glimm-Effros Theorem Through Two Graph Dichotomies

Specialeforsvar: Lukas Holter Melgaard

Titel: Classical Proofs of Silver’s Theorem and the Glimm-Effros Theorem Through Two Graph Dichotomies

Abstract: In this thesis we prove two famous results about Borel equivalence relations, Silver’s dichotomy theorem and the Glimm-Effros theorem, using methods solely from classical descriptive set theory. The main focus of the thesis will be on
presenting classical proofs of two graph dichotomies, the G0-dichotomy and the ”local” G0-dichotomy, which are then used as the main components in the proofs of Silver’s theorem and the Glimm-Effros theorem.

Vejleder: Asger D. Törnqvist
Censor:    Andreas Hallbäck