Kurt Gödel Research Center

2011 seminar talk: Rado's Conjecture and the Tree Property for ω₂

Talk held by Victor Torres (KGRC) at the KGRC seminar on 2011-03-17.

Abstract

Rado's Conjecture is the following statement: A tree T of height ω₁ is special (i.e. the union of countable many antichains) iff every subtree of T of size ℵ₁ is special. In the first part of the talk we will give a short introduction to this principle, and present some of its properties and consequences.

Recently, Rémi Strullu proved that the Map Reflection Principle plus MA imply the Tree Property for ω₂. Similarly, Laura Fontanella showed recently that the Reflection Principle together with MA imply the Tree Property for ω₂. In this talk we will present a joint work with Laura Fontanella and Lauri Tuomi, where we discuss whether Rado's Conjecture could also imply the Tree Property for ω₂.