Classical forcing axioms such as Martin s Axiom, the Proper Forcing Axiom and Martin s Maximum have been very successful in settling not only foundational set theoretic questions such as the value of the continuum, but also solve some important mathematical problems not decidable in ZFC alone. Examples are Kaplansky's conjecture on automatic continuity in Banach algebras and Whitehead s problem in homological algebra. These axioms give a fairly complete picture of the first uncountable cardinal, $\aleph_1$, but they do not say much about higher levels of the cumulative hierarchy. Higher forcing axioms is a research project which attempts to lift this situation to the second uncountable cardinal, $\aleph_2$, and beyond. The situation here is quite different and a number of technical problems and philosophical challenges arises. We will discuss the current state of affairs in this research and mention some recent results (joint with R. Mohammadpour) in this direction.
Please send an email to r.zoghi@gmail.com to join this webinar.