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Large Cardinals and Lightface Definable Wellorders without GCH
Mon 11 March 2013, 17:00
Peter Holy
University of Bristol
Organisers: Philip Welch, Peter Holy
ABSTRACT
In Goedel's constructible universe L, there exists a lightface definable wellorder of H_{kappa^+} for every infinite cardinal kappa. But those wellorders are short (as H_{kappa^+} has size 2^kappa=kappa^+ by the GCH) and L does not allow for the existence of larger large cardinals. In this talk, I present a forcing to obtain (over any model of SCH) a lightface definable wellorder of H_{kappa^+} for every inaccessible kappa, preserving failures of the GCH and all supercompact cardinals. This is joint work with Sy Friedman and Philipp Luecke.