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.