We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of 1-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with [C. Ealy, D. Haskell and J. Marikova, Residue field domination in real closed valued fields, Notre Dame J. Formal Logic 60(3) (2019) 333-351], this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.
The domination monoid in o-minimal theories
Mennuni, Rosario
2022-01-01
Abstract
We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of 1-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with [C. Ealy, D. Haskell and J. Marikova, Residue field domination in real closed valued fields, Notre Dame J. Formal Logic 60(3) (2019) 333-351], this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.File in questo prodotto:
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