A forest is a generalization of a tree, and here we consider the Aronszajn and Suslin properties for forests. We focus on those forests satisfying coherence, a local smallness property. We show that coherent Aronszajn forests can be constructed within ZFC. We give several ways of obtaining coherent Suslin forests by forcing, one of which generalizes the well-known argument of Todor\v{c}evi\'{c} that a Cohen real adds a Suslin tree. Another uses a strong combinatorial principle that plays a… Expand

In the style of the tree property, we give combinatorial principles that capture the concepts of the so-called subtle and ineffable cardinals in such a way that they are also applicable to small… Expand

A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the… Expand

It is proved that coherent families exist on κ = ω n, where n ∈ ω , and that they consistently exist for every cardinal κ, and that iterations of Axiom A forcings with countable supports areAxiom A.Expand

Studies in logic and the foundations of mathematics

1983

TLDR

The Foundations of Set Theory and Infinitary Combinatorics are presented, followed by a discussion of easy Consistency Proofs and Defining Definability.Expand

On montre que les paires d'ordinaux denombrables peuvent etre colorees avec une infinite non denombrable de couleurs de telle sorte que tout ensemble non denombrable contienne des paires de chaque… Expand

Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series
$$\displaystyle{ E_{\alpha _{1},\beta… Expand