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Model Theory of Fields

D. Marker, M. Messmer & A. Pillay

Studia Logica 67 (1):123-124 (2001)

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Co-theory of sorted profinite groups for PAC structures.Daniel Max Hoffmann & Junguk Lee - 2023 - Journal of Mathematical Logic 23 (3).details We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the “Weak Independence Theorem” for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property [Formula: see text]. Fourth, we describe Kim-dividing in (...) Download Export citation Bookmark 2 citations
Definability of derivations in the reducts of differentially closed fields.Vahagn Aslanyan - 2017 - Journal of Symbolic Logic 82 (4):1252-1277.details Download Export citation Bookmark 3 citations
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
Thorn independence in the field of real numbers with a small multiplicative group.Alexander Berenstein, Clifton Ealy & Ayhan Günaydın - 2007 - Annals of Pure and Applied Logic 150 (1-3):1-18.details We characterize þ-independence in a variety of structures, focusing on the field of real numbers expanded by predicate defining a dense multiplicative subgroup, G, satisfying the Mann property and whose pth powers are of finite index in G. We also show such structures are super-rosy and eliminate imaginaries up to codes for small sets. Download Export citation Bookmark 11 citations
On subgroups of the additive group in differentially closed fields.Sonat Süer - 2012 - Journal of Symbolic Logic 77 (2):369-391.details In this paper we deal with the model theory of differentially closed fields of characteristic zero with finitely many commuting derivations. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types which are orthogonal to fields. Then we classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal (...) Download Export citation Bookmark
Compact complex manifolds with the DOP and other properties.Anand Pillay & Thomas Scanlon - 2002 - Journal of Symbolic Logic 67 (2):737-743.details We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a Kahler manifold to be totally degenerate (that is, to be an indiscernible set, in its canonical language) and point out that there are K3 surfaces which satisfy these conditions. Download Export citation Bookmark

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