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Model theory of fields with free operators in characteristic zero. (English) Zbl 1338.03067

Summary: Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme \(\mathcal{D}\) over a field \(A\) of characteristic zero, the theory of \(\mathcal{D}\)-fields has a model companion \(\mathcal{D}\)-\(\text{CF}_{0}\) which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types.

MSC:

03C60 Model-theoretic algebra
12H05 Differential algebra
12H10 Difference algebra
12L12 Model theory of fields
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