# Thomas Johnstone

Thomas Johnstone earned his Ph.D. under my supervision in June, 2007 at the CUNY Graduate Center.  Tom likes to get thoroughly to the bottom of a problem, and this indeed is what he did in his dissertation work on the forcing-theoretic aspects of unfoldable cardinals.  He seemed to want always to dig deeper, seeking out the unstated general phenomenon behind the results.  His characteristic style of giving a seminar talk—pure mathematical pleasure to attend—is to explain not only why the mathematical fact is true, but also why the proof must be the way that it is.  Thomas holds a tenure-track position at the New York City College of Technology of CUNY.

Thomas A. Johnstone

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Thomas A. Johnstone, “Strongly unfoldable cardinals made indestructible,” Ph.D. dissertation, The Graduate Center of the City University of New York, June 2007.

Abstract. I provide indestructibility results for weakly compact, indescribable and strongly unfoldable cardinals. In order to make these large cardinals indestructible, I assume the existence of a strongly unfoldable cardinal $\kappa$, which is a hypothesis consistent with $V=L$. The main result shows that any strongly unfoldable cardinal $\kappa$ can be made indestructible by all ${<}\kappa$-closed forcing which does not collapse $\kappa^{+}$. As strongly unfoldable cardinals strengthen both indescribable and weakly compact cardinals, I obtain indestructibility for these cardinals also, thereby reducing the large cardinal hypothesis of previously known indestructibility results for these cardinals significantly. Finally, I use the developed methods to show the consistency of a weakening of the Proper Forcing Axiom $\rm PFA$ relative to the existence of a strongly unfoldable cardinal.