The even-odd hat problem
We answer a question of C. Hardin and A. Taylor concerning a hat-guessing game.
The Growth of the Subuniform Ultrafilters on ω_1
The homomorphic images of infinite symmetric groups.
The Hurewicz covering property and slaloms in the Baire space
According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This...
The Number Of Antichains Of Finite Power Sets
The number of antichains of finite power sets.
The regularity properties on the real line
The relation of rapid ultrafilters and Q-points to Van der Waerden ideal
The size of maximal almost disjoint families [Book]
The spectrum of characters of ultrafilters on ω
We show the consistency of the statement: "the set of regular cardinals which are the characters of ultrafilters on ω is not convex". We also deal with the set of π-characters of ultrafilters on ω.
The tree property at both and
We force from large cardinals a model of ZFC in which and both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model even satisfies the super tree property.
The uniqueness of Haar measure and set theory
Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits of all points...
The Σ* approach to the fine structure of L
We present a reformulation of the fine structure theory from Jensen [72] based on his Σ* theory for K and introduce the Fine Structure Principle, which captures its essential content. We use this theory to prove the Square and Fine Scale Principles, and to construct Morasses.
Theorems on sets not belonging to algebras.
There are absolute ultrafilters on N which are not minimal
Tightly packed families of sots
Topological spaces compact with respect to a set of filters
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there...
Towers of measurable functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
Transitive Properties of Ideals on Generalized Cantor Spaces
We compute transitive cardinal coefficients of ideals on generalized Cantor spaces. In particular, we show that there exists a null set such that for every null set we can find such that A ∪ (A+x) cannot be covered by any translation of B.
Two cases when and are equal
We deal with two cardinal invariants and give conditions on their equality using Shelah's pcf theory.