CONNECTEDNESS IN STRUCTURES ON THE REAL NUMBERS: O-MINIMALITY AND UNDECIDABILITY

DOI10.1017/jsl.2022.16OpenAlexW3108170844MaRDI QIDQ5100061

Alex Savatovsky, Alfred Dolich, Chris Miller, Athipat Thamrongthanyalak

Publication date: 29 August 2022

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

Full work available at URL: https://arxiv.org/abs/2011.14833

zbMATH Keywords

undecidabilitypath componento-minimalquasicomponentlocally o-minimal

Mathematics Subject Classification ID

Undecidability and degrees of sets of sentences (03D35) Connected and locally connected spaces (general aspects) (54D05) Model theory of ordered structures; o-minimality (03C64)

Cites Work

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• Locally o-minimal structures
• Model theory.
• Definable Boolean combinations of open sets are Boolean combinations of open definable sets
• Geometric categories and o-minimal structures
• Expansions of o-minimal structures by iteration sequences
• Michael's selection theorem in a semilinear context
• Expansions of o-minimal structures by sparse sets
• Expansions of o-minimal structures on the real field by trajectories of linear vector fields
• Definably connected nonconnected sets
• Structures having o-minimal open core
• First order topological structures and theories
• Expansions of dense linear orders with the intermediate value property
• Dimensional coincidence does not imply measure-theoretic tameness
• Definable continuous selections of set-valued maps in o-minimal expansions of the real field
• Michael’s Selection Theorem in d-minimal expansions of the real field
• D-minimal expansions of the real field have the zero set property
• Expansions of o-minimal structures by fast sequences
• Definability and decision problems in arithmetic

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