Strongly minimal reducts of valued fields
Piotr Kowalski, Serge Randriambololona
TL;DR
This paper proves that certain minimal reducts of algebraically closed valued fields that include addition are essentially equivalent to the entire field, revealing a strong structural rigidity.
Contribution
It establishes that strongly minimal, non-locally modular reducts containing + are bi-interpretable with the original valued field, a new rigidity result.
Findings
Reducts containing + are bi-interpretable with the field
Strongly minimal non-locally modular reducts are essentially the whole field
Structural rigidity of valued fields in model theory
Abstract
We prove that if a strongly minimal non-locally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the underlying field.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology