# 2002 seminar talk: A combinatorial proof of \Sigma^1_3 correctness of K

Talk held by Ralf Schindler (KGRC) at the KGRC seminar on 2002-01-10.

### Abstract

I'll show you a new, simple, and purely combinatorial proof of the following result, which is originally due to Steel (1993): Let the real x be a solution to the \Pi^1_2 property \Phi(-), and suppose that x^dagger exists; suppose further that there's no inner model with a Woodin cardinal. There is then a lightface mouse which contains a solution to \Phi(-).