December 8
David Marker,
University of Illinois at Chicago
Rigid real closed fields?
Every archimedean real closed field is rigid, i.e., has no nontrivial automorphisms. What happens in the non-archimedean case? Shelah showed it is consistent that there are uncountable rigid non-archimedean real closed fields. Enayat asked what happens in the countable case. I believe the question is even interesting in the finite transcendence degree case. In this talk I will describe Shelah's proof and discuss some interesting phenomenon that arises even in transcendence degree 2.