Superstrong and other large cardinals are never Laver indestructible, ASL 2014, Boulder, May 2014

The Flatirons, Boulder, ColoradoThis will be an invited talk at the ASL 2014 North American Annual Meeting (May 19-22, 2014) in the special session Set Theory in Honor of Rich Laver, organized by Bill Mitchell and Jean Larson.

Abstract.  The large cardinal indestructibility phenomenon, discovered by Richard Laver with his seminal result on supercompact cardinals, is by now often seen as pervasive in the large cardinal hierarchy. Nevertheless, a new never-indestrucible phenomenon has emerged.  Superstrong cardinals, for example, are never Laver indestructible.  Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong cardinals, uplifting cardinals, pseudo-uplifting cardinals, superstrongly unfoldable cardinals, $\Sigma_n$-reflecting cardinals, $\Sigma_n$-correct cardinals and $\Sigma_n$-extendible cardinals (all for $n\geq 3$) are never Laver indestructible.  The proof involves a detailed technical analysis of the complexity of the definition in Laver’s theorem on the definability of the ground model, thereby involving and extending results in set-theoretic geology.  This is joint work between myself and Joan Bagaria, Kostas Tasprounis and Toshimichi Usuba.

Article | Slides

Richard Laver, 1942 – 2012

Richard Laver (October 20, 1942 — September 19, 2012).  Richard Joseph Laver, celebrated mathematician, climber, bridge player, chess master, pick-up basketball player, and friend was born in Los Angeles, California to Alma Laver Makinen and Richard Burgess Laver.  Wednesday, September 19, 2012 at 2:52 in the morning in Boulder, Colorado, Rich passed away due to complications of Parkinson’s disease.  He was surrounded by loved ones.

An informal open house gathering for friends, colleagues, and associates will be held Sunday, September 23, 2012 1pm to 5pm at Rich’s house.  A memorial will be held in the more distant future.  (Contact Sheila Miller

A more detailed notice will follow.

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