Existentially closed exponential fields

Levon Haykazyan, Jonathan Kirby

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Abstract

We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amalgamation bases and characterise the types over them. We define a notion of independence and show that independent systems of higher dimension can also be amalgamated. We extend some notions from classification theory to positive logic and position the category of existentially closed exponential fields in the stability hierarchy as NSOP1 but TP2.
Original languageEnglish
Pages (from-to)89–117
Number of pages29
JournalIsrael Journal of Mathematics
Volume241
Early online date16 Jan 2021
DOIs
Publication statusPublished - Mar 2021

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