Supercompact spaces

Diagonal Supercompact Radin Forcing

In this paper we consider two methods for producing models with some global behavior of the continuum function on singular cardinals and the failure of weak square. The first method is as an extension of Sinapova’s work [21]. We define a diagonal supercompact Radin forcing which adds a club subset to a cardinal κ while forcing the failure of SCH everywhere on the club. The intuition from Sinapo...

Supercompact extender based Prikry forcing

The extender based Prikry forcing notion is being generalized to supercompact extenders.

Topology Proceedings 3 (1978) pp. 227-236: ON THE CHARACTER OF SUPERCOMPACT SPACES

Epireflections and Supercompact Cardinals

We prove that the existence of arbitrarily large supercompact cardinals implies that every absolute epireflective class of objects in a balanced accessible category is a small-orthogonality class. In other words, if L is a localization functor on a balanced accessible category such that the unit morphism X → LX is an epimorphism for all X and the class of L-local objects is defined by an absolu...

Chang’s Conjecture May Fail at Supercompact Cardinals

We prove a revised version of Laver’s indestructibility theorem which slightly improves over the classical result. An application yields the consistency of (κ, κ) ։/ (א1,א0) when κ is supercompact. The actual proofs show that ω1-regressive Kurepatrees are consistent above a supercompact cardinal even though MM destroys them on all regular cardinals. This rather paradoxical fact contradicts the ...