Supercompact minus compact is super

Exactly controlling the non-supercompact strongly compact cardinals

We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardi...

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme

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.

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...