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.
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.