33 research outputs found
Definable and invariant types in enrichments of NIP theories
Let T be an NIP L-theory and T' be an enrichment. We give a sufficient
condition on T' for the underlying L-type of any definable (respectively
invariant) type over a model of T' to be definable (respectively invariant) as
an L-type. Besides, we generalise work of Simon and Starchenko on the density
of definable types among non forking types to this relative setting. These
results are then applied to Scanlon's model completion of valued differential
fields.Comment: 9 pages. An error was pointed out in section 2 of the previous
version so that section was removed. So was Proposition 3.8 that depended on
i
Towards a Model Theory for Transseries
The differential field of transseries extends the field of real Laurent
series, and occurs in various context: asymptotic expansions, analytic vector
fields, o-minimal structures, to name a few. We give an overview of the
algebraic and model-theoretic aspects of this differential field, and report on
our efforts to understand its first-order theory.Comment: Notre Dame J. Form. Log., to appear; 33 p
Imaginaries in separably closed valued fields
We show that separably closed valued fields of finite imperfection degree
(either with lambda-functions or commuting Hasse derivations) eliminate
imaginaries in the geometric language. We then use this classification of
interpretable sets to study stably dominated types in those structures. We show
that separably closed valued fields of finite imperfection degree are
metastable and that the space of stably dominated types is strict
pro-definable