367 research outputs found
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
Amalgamation of types in pseudo-algebraically closed fields and applications
This paper studies unbounded PAC fields and shows an amalgamation result for
types over algebraically closed sets. It discusses various applications, for
instance that omega-free PAC fields have the property NSOP3. It also contains a
description of imaginaries in PAC fields.Comment: Minor changes in v3. Accepted versio
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