Submission date: 29 August 2019

Abstract:

We develop distality rank as a property of first-order theories and give examples for each rank m such that 1 ≤ m ≤ ω. For NIP theories, we show that distality rank is invariant under base change. We also define a generalization of type orthogonality called m-determinacy and show that theories of distality rank m require certain products to be m-determined. Furthermore, for NIP theories, this behavior characterizes distality rank m.

Mathematics Subject Classification: 03C45 (Primary) 03C50 (Secondary)

Keywords and phrases:

Full text arXiv 1908.11400: pdf, ps.