2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63145Steel and Welch have shown that K is Σ^1_3 correct if the reals are closed under sharps but 0^\pistol doesn't exist. We'll give a simple and purely combinatorial proof of the following: K is Σ^1_3 correct if the reals are closed under sharps, there is no inner model with a Woodin cardinal, K exists, and * holds. Here, * is an assertion which can easily be verified if 0^\pistol doesn't exist. We conjecture that * holds outright. (* is denoted by \clubsuit in the paper.)5 pagesLogic03E15;03E45;03E55text