If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(REG) fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser
1 Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the lea...
We investigate the consistency strength of the forcing axiom for Σ13 formulas, for various classes o...
In the following κ and λ are arbitrary regular uncountable cardinals. What was known? Theorem 1 (Bal...
If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(...
AbstractI use generic embeddings induced by generic normal measures on Pκ(λ) that can be forced to e...
Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardina...
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
AbstractThe large cardinal axioms of the title assert, respectively, the existence of a nontrivial e...
AbstractIn recent work, the second author extended combinatorial principles due to Jech and Magidor ...
If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategi...
We say that κ is µ-hypermeasurable (or µ-strong) for a cardinal µ ≥ κ+ if there is an embedding j: V...
In this survey paper, we will summarise some of the more and less known results on the generalisatio...
Abstract. We show that, assuming GCH, if κ is a Ramsey or a strongly Ramsey cardinal and F is a clas...
The following consists of precise formulations and several conjectures spelling out ideas that were ...
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...
We investigate the consistency strength of the forcing axiom for Σ13 formulas, for various classes o...
In the following κ and λ are arbitrary regular uncountable cardinals. What was known? Theorem 1 (Bal...
If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(...
AbstractI use generic embeddings induced by generic normal measures on Pκ(λ) that can be forced to e...
Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardina...
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
AbstractThe large cardinal axioms of the title assert, respectively, the existence of a nontrivial e...
AbstractIn recent work, the second author extended combinatorial principles due to Jech and Magidor ...
If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategi...
We say that κ is µ-hypermeasurable (or µ-strong) for a cardinal µ ≥ κ+ if there is an embedding j: V...
In this survey paper, we will summarise some of the more and less known results on the generalisatio...
Abstract. We show that, assuming GCH, if κ is a Ramsey or a strongly Ramsey cardinal and F is a clas...
The following consists of precise formulations and several conjectures spelling out ideas that were ...
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...
We investigate the consistency strength of the forcing axiom for Σ13 formulas, for various classes o...
In the following κ and λ are arbitrary regular uncountable cardinals. What was known? Theorem 1 (Bal...
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