Transfer Principles in Henselian Valued Fields

Abstract In this thesis, we study transfer principles in the context of certain Henselian valued fields, namely fields equicharacteristic $0$ , algebraically closed maximal Kaplansky and unramified mixed characteristic with perfect residue field. First, compute burden such a field terms its value group The is cardinal related to model theoretic complexity notion dimension associated $\text {NTP}_2$ theories. We show, for instance, that Hahn $\mathbb {F}_p^{\text {alg}}((\mathbb {Z}[1/p]))$ inp-minimal (of 1), ring Witt vectors $W(\mathbb {alg}})$ over {alg}}$ not strong $\omega $ ). This result extends previous work by Chernikov Simon realizes an important step toward classification finite burden. Second, show principle property all types realized given elementary extension are definable. It can be written as follows: above stably embedded if only corresponding groups, satisfies algebraic condition. power series {R}((t))$ Similarly, quotient Cubides Delon Ye. These distinct results use common approach, which has been developed recently. consists establishing first reduction intermediate structure called leading term structure, or $\operatorname {\mathrm {RV}}$ -sort, then reducing leads us develop similar pure short exact sequences abelian groups. prepared Pierre Touchard. E-mail : [email protected] URL https://miami.uni-muenster.de/Record/a612cf73-0a2f-42c4-b1e4-7d28934138a9