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V. Torres-Perez:
"Rado´s Conjecture, reflection and semi-stationary reflection principles";
Vortrag: 2nd Meeting of Mexican Mathematicians around the World, Mathematics Research Center - CIMAT, Guanajuato, Mexico (eingeladen); 15.12.2014 - 19.12.2014.

We would like to discuss a compactness principle known as Rado's Conjecture (RC). This principle states the following: A family of convex sets of a linearly ordered set is the union of countably many disjoint subfamilies if and only if each of its subfamilies of size is also the union of countably many disjoint subfamilies. This principle is not compatible with Martin's Axiom, one of the first Forcing Axioms considered. However, RC has implications similar to other well-studied Forcing Axioms such as the Proper Forcing Axiom. For exmple, RC impies the size of the continuum is at most , the Singular Cardinal Hypothesis, the negation of several square principles, the Tree Property for , etc. We would like to discuss some of our recent results involving this principle.