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Journals and Conferences
(A) We study in this paper some connections between the Fra¨ıssé theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of… (More)
This paper establishes a refinement of the classical LöwenheimSkolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order… (More)
Motivated by Tukey classification problems and building on work in Part 1 , we develop a new hierarchy of topological Ramsey spaces Rα, α < ω1. These spaces form a natural hierarchy of complexity,… (More)
We investigate the effect of forcing with a coherent Souslin trees on two standard set-theoretic dichotomies and several topological chain conditions.
We show that 1, w, ax, u x ux and ["iF" are the only cofinal types of directed sets of size S,, but that there exist many cofinal types of directed sets of size continuum. A partially ordered set D… (More)
Motivated by a Tukey classification problem we develop here a new topological Ramsey space R1 that in its complexity comes immediately after the classical Ellentuck space . Associated with R1 is… (More)
We study Tukey types of ultrafilters on ω, focusing on the question of when Tukey reducibility is equivalent to Rudin-Keisler reducibility. We give several conditions under which this equivalence… (More)
In , Todorcevic gives a survey of basis problems in combinatorial set theory, listing nine theorems and six working conjectures — all in the presence of PFA — including the following three of… (More)
We show how to force two strong positive partition relations on u, and use them in considering several well-known open problems. In  Sierpiñski proved that the well-known Ramsey Theorem  does… (More)
We introduce and study a metric notion for trees and relate it to a conjecture of Shelah  about the existence of a finite basis for a class of linear orderings.