# Beyond the Continuum: The Search for Higher Analogues of Martin’s Axiom

Set theory seminarFriday, December 11, 201510:00 amGC 3212

# Beyond the Continuum: The Search for Higher Analogues of Martin’s Axiom

### University of Bonn

Martin’s axiom has been very successful in deciding numerous questions such as the Souslin hypothesis. Can we find higher analogues that, for example, decide the $\kappa$-Souslin hypothesis and allow us to meet $< 2^\kappa$ dense open sets? If one is careful enough and imposes closure conditions and stronger forms of the $\kappa$-cc, one obtains the principle BA$_\kappa$, independently discovered by Baumgartner, Laver and Shelah. BA$_\kappa$ shares many similarities with Martin’s axiom but decides the $\kappa$-Souslin hypothesis in the wrong way.

Felix Chopra is a graduate student at the University of Bonn studying set theory and mathematical logic under the supervision of Prof. Dr. Peter Koepke.

Posted by on December 1st, 2015