Rado's Conjecture is the following statement: A tree \(T\) of height \(\omega_1\) is special (i.e. the union of countable many antichains) iff every subtree of \(T\) of size \(\aleph_1\) 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 \(\omega_2\). Similarly, Laura Fontanella showed recently that the Reflection Principle together with MA imply the Tree Property for \(\omega_2\). 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 \(\omega_2\).