Add to ORKGAbstract. An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where for every n ≥ 2 and µ ≥ ℵn, we have (ℵn, µ)-ITP. 1
We force and construct a model in which GCH and level by level equivalence between strong compactnes...
If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing ...
We construct two models containing exactly one supercompact cardinal in which all non-supercompact m...
Abstract. An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove t...
AbstractWe show relative to strong hypotheses that patterns of compact cardinals in the universe, wh...
In this paper we extend the length of the longest interval of regular cardinals which can consistent...
AbstractStarting from a supercompact cardinal κ, we force and construct a model in which κ is both t...
1 Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the lea...
AbstractWe construct a model in which there are no ℵn-Aronszajn trees for any finiten⩾2, starting fr...
We show the relative consistency of the existence of two strongly compact cardinals κ1 and κ2 which ...
Suppose λ> κ is measurable. We show that if κ is either indestructibly supercompact or indestruct...
We construct a model for the level by level equivalence between strong compactness and supercompactn...
Abstract. This paper concerns the model of Cummings and Foreman where from ω supercompact cardinals ...
Abstract. We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a ...
Abstract. We show that given ω many supercompact cardinals and a weakly compact above them, there is...
We force and construct a model in which GCH and level by level equivalence between strong compactnes...
If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing ...
We construct two models containing exactly one supercompact cardinal in which all non-supercompact m...
Abstract. An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove t...
AbstractWe show relative to strong hypotheses that patterns of compact cardinals in the universe, wh...
In this paper we extend the length of the longest interval of regular cardinals which can consistent...
AbstractStarting from a supercompact cardinal κ, we force and construct a model in which κ is both t...
1 Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the lea...
AbstractWe construct a model in which there are no ℵn-Aronszajn trees for any finiten⩾2, starting fr...
We show the relative consistency of the existence of two strongly compact cardinals κ1 and κ2 which ...
Suppose λ> κ is measurable. We show that if κ is either indestructibly supercompact or indestruct...
We construct a model for the level by level equivalence between strong compactness and supercompactn...
Abstract. This paper concerns the model of Cummings and Foreman where from ω supercompact cardinals ...
Abstract. We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a ...
Abstract. We show that given ω many supercompact cardinals and a weakly compact above them, there is...
We force and construct a model in which GCH and level by level equivalence between strong compactnes...
If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing ...
We construct two models containing exactly one supercompact cardinal in which all non-supercompact m...