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Tiltan and graphs with no infinite paths

Shimon Garti

Abstract

We prove the consistency of tiltan with the positive relation $ω^*\cdotω_1\rightarrow(ω^*\cdotω_1,{\rm infinite\ path})^2$.

Tiltan and graphs with no infinite paths

Abstract

We prove the consistency of tiltan with the positive relation .
Paper Structure (3 sections, 9 theorems, 1 equation)

This paper contains 3 sections, 9 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Background
  3. Graphs with no infinite path

Key Result

Theorem 1.1

Generalized Martin's axiom. One can force $2^{\aleph_0}=\aleph_1, 2^{\aleph_1}>\aleph_2$ and if $\mathbb{P}$ satisfies: then for every $\kappa<2^{\aleph_1}$ such that $\gamma<\kappa\Rightarrow \gamma^{\aleph_0}<\kappa$ and any collection $\mathcal{D} = \{D_\eta: \eta\in\kappa\}$ of dense subsets of $\mathbb{P}$ there exists a filter $G\subseteq\mathbb{P}$ so that $G\cap D_\eta\neq\varnothing$ for

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Theorem 1.1
  • Lemma 1.2
  • Theorem 1.3
  • Lemma 1.4
  • Definition 2.1
  • Lemma 2.2
  • Claim 2.3
  • Lemma 2.4
  • ...and 3 more