5 papers · 1 filter
Exactly controlling the non-supercompact strongly compact cardinals
Arthur W. Apter, Joel David Hamkins
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 c…
Indestructibility and the level-by-level agreement between strong compactness and supercompactness
Arthur W. Apter, Joel David Hamkins
Can a supercompact cardinal kappa be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if…
Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
Arthur W. Apter, Joel David Hamkins
We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling th…
Patterns of Compact Cardinals
Arthur W. Apter
We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be v…
Universal Indestructibility
Arthur W. Apter, Joel David Hamkins
From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact…