Quantifier Elimination for the Relative Frobenius

Quantifier Elimination for the Relative Frobenius

Analytic difference rings

Generalizing and synthesizing earlier work on the model theory of valued difference fields and on the model theory of valued fields with analytic structure, we prove Ax-Kochen-Eršov style relative completeness and relative quantifier elimination theorems for a theory of valuation rings with analytic and difference structure. Specializing our results to the case of W [F p ], the ring of Witt vec...

. Model Theory of the Frobenius on the Witt Vectors

We give axiomatizations and prove quantifier elimination theorems for first-order theories of unramified valued fields with an automorphism having a close interaction with the valuation. We achieve an analogue of the classical Ostrowski theory of pseudoconvergence. In the outstanding case of Witt vectors with their Frobenius map, we use the ∂-ring formalism from Joyal.

Quantifier Elimination for Tame Fields

In this paper, we show that the theory of tame fields of equal characteristic admits (relative) quantifier elimination in an appropriate language.

Separably Closed Fields and contractive Ore Modules

We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.