**September 13**

**David Marker**,
University of Illinois at Chicago

**Rigid real closed fields**

Shelah showed that it is consistent that there are uncountable rigid non-archimedean real closed fields and, later, he and Mekler proved this in $\textbf{ZFC}$. Answering a question of Enayat, Charlie Steinhorn and I show that there are countable rigid non-archimedean real closed fields by constructing one of transcendence degree two.