Liccardo, Martina (2022) Some model theoretic aspects of ordered abelian groups. [Tesi di dottorato]

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Item Type: Tesi di dottorato
Resource language: English
Title: Some model theoretic aspects of ordered abelian groups
Creators:
CreatorsEmail
Liccardo, Martinamartina.liccardo2@unina.it
Date: 2022
Number of Pages: 88
Institution: Università degli Studi di Napoli Federico II
Department: Matematica e Applicazioni "Renato Caccioppoli"
Dottorato: Matematica e Applicazioni
Ciclo di dottorato: 34
Coordinatore del Corso di dottorato:
nomeemail
Moscariello, GiocondaUNSPECIFIED
Tutor:
nomeemail
Festa, PaolaUNSPECIFIED
D'Aquino, PaolaUNSPECIFIED
Date: 2022
Number of Pages: 88
Keywords: ordered abelian groups; elimination of imaginaries; stable embeddedness
Settori scientifico-disciplinari del MIUR: Area 01 - Scienze matematiche e informatiche > MAT/01 - Logica matematica
Date Deposited: 24 Mar 2022 07:11
Last Modified: 28 Feb 2024 14:22
URI: http://www.fedoa.unina.it/id/eprint/14625

Collection description

This thesis is concerned with the model theory of ordered abelian groups, in relation to the properties of eliminating imaginaries and having definable types. We investigate the property of elimination of imaginaries for some special cases of ordered abelian groups. In particular, we prove that certain Hahn products of ordered abelian groups do not eliminate imaginaries in the pure language of ordered abelian groups. Moreover, we study the property for an ordered abelian group to be stably embedded (i.e. to have definable types). We identify a sufficient and necessary condition for certain ordered abelian groups to be stably embedded. These include regular ordered abelian groups, ordered abelian groups with finite regular rank and models of the theory of a maximal ordered abelian group satisfying a condition on the definability of its principal convex subgroups.

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