Uncountable Real Closed Fields with PA Integer Parts
  D'Aquino, Knight and Starchenko classified the countable real closed fields with integer parts that are nonstandard models of Peano Arithmetic. We rule out some possibilities for extending their results to the uncountable and study real closures of $\omega_1$-like models of PA. 
David Marker, James Schmerl and Charles Steinhorn
math.LO