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 NSOP1-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.
|Journal||Annals of Pure and Applied Logic|
|Early online date||15 May 2023|
|Publication status||E-pub ahead of print - 15 May 2023|
- Independence relation
- exponential field
- abstract elementary class