Existentially closed exponential fields

Jonathan Kirby, University of East Anglia. Part of the Logic Seminar Series.

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, which is the same as what category-theorists call coherent logic.

We find the amalgamation bases for exponential fields and characterise the types over them.  We define a notion of independence and show that independent 3-systems can 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 NSOP_1.

This is joint work with Levon Haykazyan.