Submission date: 13 May 2021

Abstract:

We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by Wood in the case of the theory DCF_p and that it eliminates quantifiers after adding the inverse of the Frobenius map to the language. This strengthens the results from [4]. As a by-product, we get a new geometric axiomatization of this model companion. Along the way we also prove a quantifier elimination result, which holds in a much more general context and we suggest a way of giving “one-dimensional” axiomatizations for model companions of some theories of fields with operators.

Mathematics Subject Classification: Primary 03C10, 03C60, Secondary 12H05

Keywords and phrases:

Full text arXiv 2105.06397: pdf, ps.