Liccardo, Martina (2022) Some model theoretic aspects of ordered abelian groups. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Some model theoretic aspects of ordered abelian groups |
| Autori: | Autore Email Liccardo, Martina martina.liccardo2@unina.it |
| Data: | 2022 |
| Numero di pagine: | 88 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 34 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda [non definito] |
| Tutor: | nome email Festa, Paola [non definito] D'Aquino, Paola [non definito] |
| Data: | 2022 |
| Numero di pagine: | 88 |
| Parole chiave: | ordered abelian groups; elimination of imaginaries; stable embeddedness |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/01 - Logica matematica |
| Depositato il: | 24 Mar 2022 07:11 |
| Ultima modifica: | 28 Feb 2024 14:22 |
| URI: | http://www.fedoa.unina.it/id/eprint/14625 |
Abstract
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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