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.
2022
Mennuni, Rosario
File in questo prodotto:
File Dimensione Formato  
mennuni-2021-the-domination-monoid-in-o-minimal-theories.pdf

non disponibili

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - accesso privato/ristretto
Dimensione 433.27 kB
Formato Adobe PDF
433.27 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
2008.01770v1.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 923.89 kB
Formato Adobe PDF
923.89 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1262190
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 3
social impact