1 results
MODEL THEORY OF DERIVATIONS OF THE FROBENIUS MAP REVISITED
- Part of
-
- Journal:
- The Journal of Symbolic Logic / Volume 88 / Issue 3 / September 2023
- Published online by Cambridge University Press:
- 10 November 2021, pp. 1213-1229
- Print publication:
- September 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
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
$\operatorname {DCF}_p$ 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.
