O riešení niektorých nerozhodnutelných topologických problémov
On a problem of Erdös and Tarski
On a Problem of Silver
On a theorem of Jones and Heath concerning separable normal spaces
On Cartesian Powers of a Rational Group.
On club-like principles on regular cardinals above
On families of Lindelöf and related subspaces of
We consider the families of all subspaces of size ω₁ of (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used...
On full Suslin trees
On Helling cardinals
On inaccessible cardinal numbers.
On isomorphism classes of spaces
We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces , the topological sums of Cantor cubes , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.
On iterated forcing for successors of regular cardinals
We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder...
On level by level equivalence and inequivalence between strong compactness and supercompactness
We prove two theorems, one concerning level by level inequivalence between strong compactness and supercompactness, and one concerning level by level equivalence between strong compactness and supercompactness. We first show that in a universe containing a supercompact cardinal but of restricted size, it is possible to control precisely the difference between the degree of strong compactness and supercompactness that any measurable cardinal exhibits. We then show that in an unrestricted size universe...
On nonmonotone inductive definability
On reflection of stationary sets
We show that there are stationary subsets of uncountable spaces which do not reflect.
On saturated almost disjoint families
On saturated sets of ideals and Ulam's problem
On some combinatorial problems involving large cardinals
On squares, outside guessing of clubs and I
On Supernormal Ehresmann-Dedecker Universes.