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Pseudo real closed fields, pseudo p-adically closed fields and NTP2

Samaria Montenegro

Annals of Pure and Applied Logic 168 (1):191-232 (2017)

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Definable V-topologies, Henselianity and NIP.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Journal of Mathematical Logic 20 (2):2050008.details We initiate the study of definable [Formula: see text]-topologies and show that there is at most one such [Formula: see text]-topology on a [Formula: see text]-henselian NIP field. Equivalently, we show that if [Formula: see text] is a bi-valued NIP field with [Formula: see text] henselian, then [Formula: see text] and [Formula: see text] are comparable. As a consequence, Shelah’s conjecture for NIP fields implies the henselianity conjecture for NIP fields. Furthermore, the latter conjecture is proved for any field admitting (...) Download Export citation Bookmark 5 citations
Burden in Henselian valued fields.Pierre Touchard - 2023 - Annals of Pure and Applied Logic 174 (10):103318.details Download Export citation Bookmark 1 citation
Topological properties of definable sets in ordered Abelian groups of burden 2.Alfred Dolich & John Goodrick - 2023 - Mathematical Logic Quarterly 69 (2):147-164.details We obtain some new results on the topology of unary definable sets in expansions of densely ordered Abelian groups of burden 2. In the special case in which the structure has dp‐rank 2, we show that the existence of an infinite definable discrete set precludes the definability of a set which is dense and codense in an interval, or of a set which is topologically like the Cantor middle‐third set (Theorem 2.9). If it has burden 2 and both an infinite (...) Download Export citation Bookmark
On the antichain tree property.JinHoo Ahn, Joonhee Kim & Junguk Lee - 2022 - Journal of Mathematical Logic 23 (2).details In this paper, we investigate a new model theoretical tree property (TP), called the antichain tree property (ATP). We develop combinatorial techniques for ATP. First, we show that ATP is always witnessed by a formula in a single free variable, and for formulas, not having ATP is closed under disjunction. Second, we show the equivalence of ATP and [Formula: see text]-ATP, and provide a criterion for theories to have not ATP (being NATP). Using these combinatorial observations, we find algebraic examples (...) Download Export citation Bookmark 1 citation
Definability of types and VC density in differential topological fields.Françoise Point - 2018 - Archive for Mathematical Logic 57 (7-8):809-828.details Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2. Download Export citation Bookmark 1 citation
Imaginaries in bounded pseudo real closed fields.Samaria Montenegro - 2017 - Annals of Pure and Applied Logic 168 (10):1866-1877.details Download Export citation Bookmark
Finite undecidability in PAC and PRC fields.Brian Tyrrell - 2024 - Annals of Pure and Applied Logic 175 (10):103465.details Download Export citation Bookmark

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