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Notes on local o‐minimality
Mathematical Logic Quarterly 55 (6):617-632 (2009)
Abstract
We introduce and study some local versions of o-minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functionsMy notes
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Citations of this work
Uniformly locally o-minimal structures and locally o-minimal structures admitting local definable cell decomposition.Masato Fujita - 2020 - Annals of Pure and Applied Logic 171 (2):102756.
Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind.Masato Fujita - 2020 - Journal of Symbolic Logic 85 (4):1654-1663.
Locally o-Minimal Structures with Tame Topological Properties.Masato Fujita - 2023 - Journal of Symbolic Logic 88 (1):219-241.
Tameness of definably complete locally o‐minimal structures and definable bounded multiplication.Masato Fujita, Tomohiro Kawakami & Wataru Komine - 2022 - Mathematical Logic Quarterly 68 (4):496-515.
Locally o-minimal structures and structures with locally o-minimal open core.Antongiulio Fornasiero - 2013 - Annals of Pure and Applied Logic 164 (3):211-229.
References found in this work
On ℵ0-categorical weakly o-minimal structures.B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss - 1999 - Annals of Pure and Applied Logic 101 (1):65-93.
On aleph0.B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss - 1999 - Annals of Pure and Applied Logic 101 (1):65-94.
A Guide to Classical and Modern Model Theory.Annalisa Marcja & Carlo Toffalori - 2003 - Dordrecht, Netherland: Springer.
Abrusci, VM and Ruet, P., Non-commutative logic I: the multiplicative fragment (1) 29} 64 Bridges, D., Richman, F. and Schuster, P., Linear independence without choice (1) 95} 102 Creed, P. and Truss, JK, On o-amorphous sets (2} 3) 185} 226. [REVIEW]B. Herwig, H. D. Macpherson, G. Martin & A. Nurtazin - 1999 - Annals of Pure and Applied Logic 101 (1):299.
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