Ma and lattice partitions
MAD families and -points
The Katětov ordering of two maximal almost disjoint (MAD) families and is defined as follows: We say that if there is a function such that for every . In [Garcia-Ferreira S., Hrušák M., Ordering MAD families a la Katětov, J. Symbolic Logic 68 (2003), 1337–1353] a MAD family is called -uniform if for every , we have that . We prove that CH implies that for every -uniform MAD family there is a -point of such that the set of all Rudin-Keisler predecessors of is dense in the...
MAD families with strong combinatorial properties
In his paper in Fund. Math. 178 (2003), Miller presented two conjectures regarding MAD families. The first is that CH implies the existence of a MAD family that is also a σ-set. The second is that under CH, there is a MAD family concentrated on a countable subset. These are proved in the present paper.
Martinaxiom und die Beschreibung gewisser Homomorphismen in der Theorie der N1-freien Abelschen Gruppen.
Martin's axiom and partitions
Martin's Axiom Implies the Existence of Certain Slender Groups.
Maximal almost disjoint families of functions
We study maximal almost disjoint (MAD) families of functions in that satisfy certain strong combinatorial properties. In particular, we study the notions of strongly and very MAD families of functions. We introduce and study a hierarchy of combinatorial properties lying between strong MADness and very MADness. Proving a conjecture of Brendle, we show that if , then there no very MAD families. We answer a question of Kastermans by constructing a strongly MAD family from = . Next, we study the...
Maximal σ-independent families
Measurable Functions and Almost Continuous Functions.
Measurable spaces with c.c.c. [Book]
Mesurable Outer Kernels Of Sets
Minimal predictors in hat problems
We consider a combinatorial problem related to guessing the values of a function at various points based on its values at certain other points, often presented by way of a hat-problem metaphor: there are a number of players who will have colored hats placed on their heads, and they wish to guess the colors of their own hats. A visibility relation specifies who can see which hats. This paper focuses on the existence of minimal predictors: strategies guaranteeing at least one player guesses correctly,...
More on tie-points and homeomorphism in ℕ*
A point x is a (bow) tie-point of a space X if X∖x can be partitioned into (relatively) clopen sets each with x in its closure. We denote this as where A, B are the closed sets which have a unique common accumulation point x. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of βℕ = ℕ* (by Veličković and Shelah Steprans) and in the recent study (by Levy and Dow Techanie) of precisely 2-to-1 maps on ℕ*. In these cases the tie-points have been the unique fixed point...
Multiple gaps
We study a higher-dimensional version of the standard notion of a gap formed by a finite sequence of ideals of the quotient algebra 𝓟(ω)/fin. We examine different types of such objects found in 𝓟(ω)/fin both from the combinatorial and the descriptive set-theoretic side.