Independence relations for exponential fields

Vahagn Aslanyan, Robert Henderson, Mark Kamsma, Jonathan Kirby

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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
Issue number8
Early online date15 May 2023
Publication statusPublished - Aug 2023


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

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