A cardinal preserving immune partition of the ordinals
A classification of definable forcings on ω1
Under the assumption of the existence of sharps for reals all simply definable posets on are classified up to forcing equivalence.
A large cardinal in the constructible universe
A new construction of a Kurepa tree with no Aronszajn subtree
A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.
A topological application of flat morasses
We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points of cardinality , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.
Abelian group extensions and the axiom of constructibility.