We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi-Magidor theorem from [22], i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact car...

The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible b...

The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible b...

We extend some large cardinal axioms of Jensen to weakly inaccessible cardinals. Related problems regarding the saturatedness of certain filters are also studied.

We prove that every compact space X is a Čech-Stone compactification of a normal subspace of cardinality at most d(X)t(X), and some facts about cardinal invariants of compact spaces.

In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...