Collection Model Theory and Valued Fields
Organizer(s)
Date(s)
05/03/2018
- 09/03/2018
Multi-valued algebraically closed fields are NTP₂.
By Will Johnson
Consider the expansion of an algebraically closed field K by ? arbitrary valuation rings (encoded as unary predicates). We show that the resulting structure does not have the second tree property, and is in fact strong. Along the way, we observe that the theory of algebraically closed fields with n valuations is decidable. This talk will outline the model-theoretic analysis of the case of independent non-trivial valuation rings, and sketch how the proof generalizes to the situation of arbitrary valuation rings.
