Expansions of the real field by open sets: definability versus interpretability

DOI10.2178/jsl/1286198148zbMath1220.03030arXiv0812.0836OpenAlexW2950139212MaRDI QIDQ3066795

Krzysztof Kurdyka, Harvey M. Friedman, Chris Miller, Patrick Speissegger

Publication date: 12 January 2011

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

Full work available at URL: https://arxiv.org/abs/0812.0836

zbMATH Keywords

Cantor setHausdorff dimensionMinkowski dimensionprojective hierarchyexpansion of the real fieldBorel isomorpho-minimal expansions of the real field

Mathematics Subject Classification ID

Descriptive set theory (03E15) Model theory of ordered structures; o-minimality (03C64) Other connections with logic and set theory (28E15)

Related Items (8)

Interpreting the monadic second order theory of one successor in expansions of the real line ⋮ Fractals and the monadic second order theory of one successor ⋮ Mini-workshop: Topological and differential expansions of o-minimal structures. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ A dichotomy for expansions of the real field ⋮ How to avoid a compact set ⋮ D-minimal expansions of the real field have the zero set property ⋮ A tetrachotomy for expansions of the real ordered additive group ⋮ Metric dimensions and tameness in expansions of the real field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric categories and o-minimal structures
• Expansions of o-minimal structures by iteration sequences
• Expansions of o-minimal structures by sparse sets
• Differential equations over polynomially bounded o-minimal structures
• Expansions of o-minimal structures by fast sequences

This page was built for publication: Expansions of the real field by open sets: definability versus interpretability