On dp-minimal ordered structures

DOI10.2178/jsl/1305810758zbMath1220.03037arXiv0909.4242OpenAlexW2962683765MaRDI QIDQ3011114

Pierre Simon

Publication date: 28 June 2011

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.4242

zbMATH Keywords

dp-minimalitydp-minimal groups

Mathematics Subject Classification ID

Model theory of ordered structures; o-minimality (03C64)

Related Items (34)

Externally definable quotients and NIP expansions of the real ordered additive group ⋮ Tame topology over definable uniform structures ⋮ Pseudo real closed fields, pseudo \(p\)-adically closed fields and \(\mathrm{NTP}_{2}\) ⋮ CONVEXLY ORDERABLE GROUPS AND VALUED FIELDS ⋮ The canonical topology on dp-minimal fields ⋮ Distality in valued fields and related structures ⋮ Vapnik-Chervonenkis density in some theories without the independence property. II ⋮ Non-forking and preservation of NIP and dp-rank ⋮ Theories without the tree property of the second kind ⋮ Interpretable fields in various valued fields ⋮ Pathological examples of structures with o‐minimal open core ⋮ On VC-minimal fields and dp-smallness ⋮ Burden in Henselian valued fields ⋮ Weakly binary expansions of dense meet‐trees ⋮ Topological properties of definable sets in ordered Abelian groups of burden 2 ⋮ DECIDABILITY AND CLASSIFICATION OF THE THEORY OF INTEGERS WITH PRIMES ⋮ Some Remarks on dp-Minimal Groups ⋮ Some remarks on inp-minimal and finite burden groups ⋮ Hereditary G-compactness ⋮ On Vapnik‐Chervonenkis density over indiscernible sequences ⋮ The \(\aleph_{0}\)-categorical trees ⋮ Definable sets containing productsets in expansions of groups ⋮ DP-MINIMAL VALUED FIELDS ⋮ Strict independence ⋮ Vapnik-Chervonenkis density in some theories without the independence property, I ⋮ Stationarily ordered types and the number of countable models ⋮ HENSELIAN VALUED FIELDS AND inp-MINIMALITY ⋮ Witnessing dp-rank ⋮ VC-density for trees ⋮ Linear orders in NIP structures ⋮ Defining integer-valued functions in rings of continuous definable functions over a topological field ⋮ Additivity of the dp-rank ⋮ AROUND RUBIN’S “THEORIES OF LINEAR ORDER” ⋮ Does weak quasi-o-minimality behave better than weak o-minimality?

Cites Work

• Theories of linear order
• On variants of \(o\)-minimality
• Partially ordered sets and the independence property
• An example of a 𝐶-minimal group which is not abelian-by-finite
• A monotonicity theorem for dp-minimal densely ordered groups

This page was built for publication: On dp-minimal ordered structures