# Blog Archives

# Topic Archive: 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.