Journal of the Mathematical Society of Japan

Locally o-minimal structures

Tomohiro KAWAKAMI, Kota TAKEUCHI, Hiroshi TANAKA, and Akito TSUBOI

Full-text: Open access

Abstract

In this paper we study (strongly) locally o-minimal structures. We first give a characterization of the strong local o-minimality. We also investigate locally o-minimal expansions of (R, +, <).

Article information

Source
J. Math. Soc. Japan, Volume 64, Number 3 (2012), 783-797.

Dates
First available in Project Euclid: 24 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1343133743

Digital Object Identifier
doi:10.2969/jmsj/06430783

Mathematical Reviews number (MathSciNet)
MR2965427

Zentralblatt MATH identifier
1259.03051

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality

Keywords
local o-minimality cell decomposition simple products

Citation

KAWAKAMI, Tomohiro; TAKEUCHI, Kota; TANAKA, Hiroshi; TSUBOI, Akito. Locally o-minimal structures. J. Math. Soc. Japan 64 (2012), no. 3, 783--797. doi:10.2969/jmsj/06430783. https://projecteuclid.org/euclid.jmsj/1343133743


Export citation

References

  • L. van den Dries, Tame Topology and o-minimal Structures, London Math. Soc. Lecture Note Ser., 248, Cambridge University Press, 1998.
  • L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J., 84 (1996), 497–540.
  • J. F. Knight, A. Pillay and C. Steinhorn, Definable sets in ordered structures, II, Trans. Amer. Math. Soc., 295 (1986), 593–605.
  • D. Macpherson, D. Marker and C. Steinhorn, Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc., 352 (2000), 5435–5483.
  • A. Marcja and C. Toffalori, A Guide to Classical and Modern Model Theory, Trends in Logic – Studia Logica Library, 19, Kluwer Academic Publishers, Dordrecht, 2003.
  • M. Shiota, Geometry of Subanalytic and Semialgebraic Sets, Progr. Math., 150, Birkhäuser, 1997.
  • H. Tanaka and T. Kawakami, $C^r$ strong cell decompositions in non-valuational weakly o-minimal real closed fields, Far East J. Math. Sci. (FJMS), 25 (2007), 417–431.
  • C. Toffalori and K. Vozoris, Notes on local o-minimality, MLQ Math. Log. Q., 55 (2009), 617–632.
  • R. Wencel, Weakly o-minimal non-valuational structures, Ann. Pure Appl. Logic, 154 (2008), 139–162.