On internality and the canonical base property

Abstract: This thesis contributes to the understanding of almost internality with respect to invariant families of types in a superstable theory of finite Lascar rank and was motivated by the so-called canonical base property (in short, CBP).

Influenced by work of Chatzidakis and Moosa-Pillay, we study two weakenings of the CBP, namely transfer of internality to intersections, resp. to quotients, with respect to invariant families of types of Lascar rank one. Transfer of internality to intersections is a special case of transfer to quotients. We prove that transfer of internality to quotients with respect to the family of all minimal types already implies the CBP.

We give an alternative presentation of the uncountably categorical counterexample to the CBP produced by Hrushovski, Palacin and Pillay as an additive cover of the complex numbers. We prove that this structure does not even transfer internality to intersections with respect to the unique (up to non-orthogonality) strongly minimal set, giving another reason for the failure of the CBP.

Furthermore, we begin a structural study of groups of finite Lascar rank definable in theories which transfer internality to quotients and obtain as a consequence infinitely many new additive covers of the complex numbers without the CBP

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch
• Anmerkungen: Universität Freiburg, Dissertation, 2022

Klassifikation und Themen

• Schlagwort: Property ; Modelltheorie ; Lascar

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wo): Freiburg
• (wer): Universität
• (wann): 2022
• Urheber: Lösch, Michael
• Beteiligte Personen und Organisationen: Martin-Pizarro, Amador ; Martin-Pizarro, Amador ; Moosa, Rahim ; Albert-Ludwigs-Universität Freiburg. Abteilung für Mathematische Logik ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Weitere Informationen

• DOI: 10.6094/UNIFR/229012
• URN: urn:nbn:de:bsz:25-freidok-2290128
• Rechteinformation: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 25.03.2025, 13:45 MEZ