-ideals and -gaps in the Boolean algebras Ρ(ω)/I.
Factorization theorems for strong maps between matroids of arbitrary cardinality
In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.
Filter games on ω and the dual ideal
We continue the efforts to characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorial or structural properties of the given filter. Previous results in the literature included those games where player II responded with natural numbers, or finite subsets of natural numbers. In this paper we concentrate on games where player II responds with members of the dual ideal. We also give a summary of known results on filter games.
Filtres: mesurabilité, rapidité, propriété de Baire forte
Finite Embeddability of Sets and Ultrafilters
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Čech...
Finite functions and the necessary use of large cardinals.
Flipping properties and supercompact cardinals
Forcing tightness in products of fans
We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.
Fragments of strong compactness, families of partitions and ideal extensions
We investigate some natural combinatorial principles related to the notion of mild ineffability, and use them to obtain new characterizations of mild ineffable and weakly compact cardinals. We also show that one of these principles may be satisfied by a successor cardinal. Finally, we establish a version for of the canonical Ramsey theorem for pairs.
Fraïssé structures and a conjecture of Furstenberg
We study problems concerning the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Furstenberg and a counter-conjecture by Pestov regarding the difference between , the Samuel compactification, and , the enveloping semigroup of the universal minimal flow. We resolve Furstenberg’s problem for several automorphism groups and give a detailed study in the case of , leading us to define and investigate several new types...
Free Power or Width of some Kinds of Mathematical Structures
Functions having stationary constant sets