Submission date: 20 April 2019

Abstract:

We give a new characterization of SOP (the strict order property) and an optimal version of a theorem of Shelah, namely a theory has OP (the order property) if and only if it has IP (the independence property) or SOP. We point out some parallels between dividing lines in unstable theories and subclasses of Baire 1 functions.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1904.09486: pdf, ps.