Model theory of fields with free operators in characteristic zero

Rahim Moosa, Thomas Scanlon

Published 2012-12-23, updated 2013-08-28Version 2

Generalising and unifying the known theorems for difference and differential fields, it is shown that for every finite free ${\mathbb S}$-algebra ${\mathcal D}$ over a field $A$ of characteristic zero the theory of ${\mathcal D}$-fields has a model companion ${\mathcal D}$-CF$_0$ which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types.