A characterization of determinacy for Turing degree games
A characterization of lifting generics for Sacks-like forcings
A consistency result on weak reflection
A fine hierarchy of partition cardinals
A large cardinal in the constructible universe
A new large cardinal and Laver sequences for extendibles
We define a new large cardinal axiom that fits between and in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.
A new proof of a theorem of Balcerzyk, Białynicki-Birula and Łoś
A note on a question of Abe
Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V-ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.
A Note on Indestructibility and Strong Compactness
If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing which is also (κ⁺,∞)-distributive and λ is supercompact, then by a result of Apter and Hamkins [J. Symbolic Logic 67 (2002)], δ < κ | δ is δ⁺ strongly compact yet δ is not δ⁺ supercompact must be unbounded in κ. We show that the large cardinal hypothesis on λ is necessary by constructing a model containing a supercompact cardinal κ in which no cardinal δ > κ is supercompact, κ’s supercompactness...
A note on strong compactness and resurrectibility
We construct a model containing a proper class of strongly compact cardinals in which no strongly compact cardinal ĸ is supercompact and in which every strongly compact cardinal has its strong compactness resurrectible.
A note on the Ramsey-type theorem of Erdös
A note on the λ-Shelah property
A Reduction in Consistency Strength for Universal Indestructibility
We show how to reduce the assumptions in consistency strength used to prove several theorems on universal indestructibility.
A saturation property on ideals
A splitting theorem for ℱ-products
A theorem on polarised partition relations for singular cardinals
Abelian group extensions and the axiom of constructibility.
Adding a lot of Cohen reals by adding a few. II
We study pairs (V, V₁), V ⊆ V₁, of models of ZFC such that adding κ-many Cohen reals over V₁ adds λ-many Cohen reals over V for some λ > κ.
Algorithmic representations of Wermus' constructions of ordinal numbers
An algebraic and logical approach to continuous images