# 2011 seminar talk: Rado's Conjecture and the Tree Property for *ω*_{2}

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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
*ω _{1}* is special (i.e. the union of countable many antichains) iff
every subtree of

*T*of size

*ℵ*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.

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Recently, Rémi Strullu proved that the Map Reflection Principle plus
MA imply the Tree Property for *ω _{2}*. Similarly, Laura Fontanella
showed recently that the Reflection Principle together with MA imply
the Tree Property for

*ω*. 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

_{2}*ω*.

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