A categorical characterization of sets among classes
A Corson compact L-space from a Suslin tree
The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.
A dichotomy for P-ideals of countable sets
A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra / but also on some higher order statements like for example the existence of Jensen square sequences.
A number-theoretic conjecture and its implication for set theory.
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.
A tree axiom.
Almost disjoint families and “never” cardinal invariants
We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to under the effective weak diamond principle , answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property in spaces from almost disjoint families,...
An algebraic and logical approach to continuous images