Submission date: 23 May 2012.

Abstract:

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.

Mathematics Subject Classification: 03C64 , 03C60

Keywords and phrases: Real closed field, integer part, Peano Arithmetic, recursive saturation, \omega_1-like model

Full text arXiv 1205.5156: pdf, ps.