Expansions of o-minimal structures by dense independent sets

DOI10.1016/j.apal.2016.04.003zbMath1432.03070OpenAlexW2342806294MaRDI QIDQ287480

Chris Miller, Alfred Dolich, Charles I. Steinhorn

Publication date: 20 May 2016

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2016.04.003

zbMATH Keywords

densely ordered groupeliminate imaginariesindependent predicateo-minimal structuresopen core

Mathematics Subject Classification ID

Ordered groups (group-theoretic aspects) (20F60) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Model theory of ordered structures; o-minimality (03C64) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (20)

Unnamed Item ⋮ Generic trivializations of geometric theories ⋮ Orbits of subsets of the monster model and geometric theories ⋮ Wild theories with o-minimal open core ⋮ Pathological examples of structures with o‐minimal open core ⋮ CP‐generic expansions of models of Peano Arithmetic ⋮ Product cones in dense pairs ⋮ HAMEL SPACES AND DISTAL EXPANSIONS ⋮ Supersimple structures with a dense independent subset ⋮ Distal and non‐distal behavior in pairs ⋮ Neutrally expandable models of arithmetic ⋮ Geometric structures with a dense independent subset ⋮ Structure theorems in tame expansions of o-minimal structures by a dense set ⋮ The choice property in tame expansions of o‐minimal structures ⋮ Pairs of theories satisfying a Mordell–Lang condition ⋮ DISTAL AND NON-DISTAL PAIRS ⋮ Fields with a dense-codense linearly independent multiplicative subgroup ⋮ Metric dimensions and tameness in expansions of the real field ⋮ Small sets in dense pairs ⋮ CHARACTERIZING O-MINIMAL GROUPS IN TAME EXPANSIONS OF O-MINIMAL STRUCTURES

Cites Work

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• On lovely pairs of geometric structures
• Dp-minimality: basic facts and examples
• Geometric structures with a dense independent subset
• Set theory. An introduction to independence proofs
• Generic structures and simple theories
• Definable Boolean combinations of open sets are Boolean combinations of open definable sets
• Thorn independence in the field of real numbers with a small multiplicative group
• Additivity of the dp-rank
• Generic trivializations of geometric theories
• Strong theories of ordered Abelian groups
• The independence property in generalized dense pairs of structures
• Interpreting the projective hierarchy in expansions of the real line
• The Undecidability of Algebraic Rings and Fields
• Avoiding the projective hierarchy in expansions of the real field by sequences
• Definable Sets in Ordered Structures. III
• Structures having o-minimal open core
• First order topological structures and theories
• Definable Sets in Ordered Structures. I
• Definable Sets in Ordered Structures. II
• Weakly o-minimal structures and real closed fields
• On o-minimal expansions of Archimedean ordered groups
• Extensions of ordered theories by generic predicates
• Characterizing rosy theories
• Properties and consequences of Thorn-independence
• Elimination of imaginaries in expansions of o-minimal structures by generic sets

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