Submission date: 6 November 2022

Abstract:

We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, showing that two of these are NSOP_1-like and non-simple, a third is stable, and the fourth is the quasiminimal pregeometry of Zilber's exponential fields, previously known to be stable (and uncountably categorical). We also characterise the fourth independence relation in terms of the third, strong independence.

Mathematics Subject Classification: 03C45, 03C65, 03C48

Keywords and phrases:

Full text arXiv 2211.03071: pdf, ps.