Unprepared Indestructibility

Abstract

This article is based on the talk of the same name which I gave at the "Aspects of Descriptive Set Theory" RIMS Symposium in Kyoto in October 2011; it is essentially just a survey of my article "Indestructibility of Vopenka's Principle". In particular, I present (with a sketch of the proof) a forcing indestructibility theorem for the large cardinal axiom Vopenka's Principle. It is notable in that there is no preparatory forcing required to make the axiom indestructible, unlike other indestructibility results.

arXiv comment7 pages. Survey of arXiv:1003.4707. To appear in Proceedings of the RIMS Symposium on Aspects of Descriptive Set Theory, 2011, RIMS Ko-kyu-roku series