# The distance between V and L under a strengthening of the assumption that there exists a Measurable Cardinal

#### by Zachiri McKenzie

Institution: The University of Melbourne
Date: Wed 28th May 2008
Time: 4:15 PM
Location: Room 215 Richard Berry Bldg, The University of Melbourne

Abstract: An important breakthrough in the study of large cardinal hypotheses
was the realization, made by Scott, that if a Measurable Cardinal exists,
then V 6= L. A strictly stronger assumption is the existence of a Strongly
Compact Cardinal. Under this assumption VopË‡enka and HrbaË‡cek were able
to strengthen Scotts theorem and show that for all A, V 6= L[A]. In this
talk I will introduce the concept of a Strongly Compact Cardinal and go
through VopË‡enka and HrbaË‡cekâ€™s proof of this strengthening.