Talks Summer Semester 2025
10 Apr - Leon Gitik.
17 Apr - Stefan Ludwig.
24 April - Akash Hossain. Forking in pure short exact sequences
Literature on model theory of Henselian valued fields usually establishes,
or relies on transfer principles between the theory of a valued field, and
that of its value group Gamma and residue field k. Recent contributions
often use an alternative approach, which is to study transfer principles
with an intermediate reduct of the valued field: the *leading-term
structure* RV, the expansion of the Abelian group sitting in the pure short
exact sequence (PSES, for short):
1->k*->RV->Gamma->0
The cleanest, most natural and most general framework to study this
structure is that developed in Section 4 of the very influential (and
recent) article by Aschenbrenner-Chernikov-Gehret-Ziegler: the setting of
PSES of *Abelian structures*, with an arbitrary expansion on their term on
the left and the right (such as the order on Gamma and addition on k). The
aforementioned article establishes transfer principles for *quantifier
elimination* and *distality* between the middle term (RV), and the two
other terms (Gamma, k). Thanks to this very general setting, those results
carry over for free to natural expansions of valued field (by a derivation,
an automorphism...).
In this talk, we present our contribution to this work, where we establish
similar transfer principles for *forking and dividing *in the same setting
of expansions of PSES of Abelian structures.