Author: Philipp Schlicht Title: Thin Projective Equivalence Relations and Inner Models Abstract: Greg Hjorth proved in 1993 under the assumption that all reals have sharps, that for an inner model M, M has representatives of all equivalence classes of all thin \Pi^1_2 equivalence relations if and only if M is \Sigma^1_3 correct in V and computes \omega_1 correctly. I will present a similar description of the inner models that have representatives of all equivalence classes of all thin \Pi^1_2n equivalence relations, assuming PD. These are exactly the inner models that are \Sigma^1_(2n+1)-correct in V and compute the canonical tree from a \Pi^1_(2n-1)-scale correctly. This is joint work with Greg Hjorth and Ralf Schindler.