Coherent forests.

  title={Coherent forests.},
  author={Monroe Eskew},
  journal={arXiv: Logic},
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… 



Subtle and Ineffable Tree Properties

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

A dichotomy for P-ideals of countable sets

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

On coherent families of finite-to-one functions

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.

Set theory - an introduction to independence proofs

  • K. Kunen
  • Mathematics
    Studies in logic and the foundations of mathematics
  • 1983
The Foundations of Set Theory and Infinitary Combinatorics are presented, followed by a discussion of easy Consistency Proofs and Defining Definability.

Partitioning pairs of countable ordinals

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

Multi-index Mittag-Leffler Functions

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

Some combinatorial problems concerning uncountable cardinals

Set theory. The third millennium edition, revised and expanded

  • 2003

Ulam's measure problem, saturated ideals, and cardinal arithmetic