2,432 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
F-structures and integral points on semiabelian varieties over finite fields
Motivated by the problem of determining the structure of integral points on
subvarieties of semiabelian varieties defined over finite fields, we prove a
quantifier elimination result for certain modules over finite simple extensions
of the integers given together with predicates for orbits of the distinguished
generator of the ring.Comment: 33 pages, correction made to authors' informatio
The model theory of Commutative Near Vector Spaces
In this paper we study near vector spaces over a commutative from a model
theoretic point of view. In this context we show regular near vector spaces are
in fact vector spaces. We find that near vector spaces are not first order
axiomatisable, but that finite block near vector spaces are. In the latter case
we establish quantifier elimination, and that the theory is controlled by which
elements of the pointwise additive closure of are automorphisms of the near
vector space
- …