Independence relations for exponential fields

Vahagn Aslanyan, Robert Henderson, Mark Kamsma, Jonathan Kirby

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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 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.
Original languageEnglish
Article number103288
JournalAnnals of Pure and Applied Logic
Volume174
Issue number8
Early online date15 May 2023
DOIs
Publication statusPublished - Aug 2023

Keywords

  • Independence relation
  • exponential field
  • Ax-Schanuel
  • abstract elementary class

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