Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T21:57:38.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Fusing o-minimal structures

Published online by Cambridge University Press:  12 March 2014

A.J. Wilkie
A.J. Wilkie*
Affiliation:
Mathematical Institute, University of Oxford, 24-29 ST Giles, Oxford OX1 3LB, UK, E-mail: wilkie@maths.ox.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

In this note I construct a proper o-minimal expansion of the ordered additive group of rationals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 271 - 281
Copyright
Copyright © Association for Symbolic Logic 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Edmundo, M., Structure theorems for o-minimal expansions of groups, Annals of Pure and Applied Logic, vol. 102 (2000), pp. 159–181.CrossRefGoogle Scholar
[2]Gabrielov, A., Projections of semianalytic sets, Functional Analysis and its applications, vol. 2 (1968), pp. 282–291.CrossRefGoogle Scholar
[3]Gabrielov, A., Complements of subanalytic sets and existential formulas for analytic functions, Inventiones Mathematicae, vol. 125 (1996), pp. 1–12.CrossRefGoogle Scholar
[4]Knight, J., Pillay, A., and Steinhorn, C., Definable sets in ordered structures. II, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 593–605.CrossRefGoogle Scholar
[5]Laskowski, M. C. and Steinhorn, C., On o-minimal expansions of Archimedean ordered groups, this Journal, vol. 60 (1995), pp. 817–831.Google Scholar
[6]Marker, D., Peterzil, Y., and Pillay, A., Additive reducts of real closed fields, this Journal, vol. 57 (1992). pp. 109–117.Google Scholar
[7]Miller, C. and Starchenko, S., A growth dichotomy for o-minimal expansions of ordered groups, Transactions of the American Mathematical Society, vol. 350 (1998), pp. 3505–3521.CrossRefGoogle Scholar
[8]Peterzil, Y., A structure theorem for semibounded sets in the reals, this Journal, vol. 57 (1992), pp. 779–794.Google Scholar
[9]Peterzil, Y., Reducts of some structures over the reals, this Journal, vol. 58 (1993), pp. 955–966.Google Scholar
[10]Peterzil, Y. and Starchenko, S., On torsion-free groups in o-minimal structures, preprint (09, 2003).Google Scholar
[11]Pillay, A., Scowcroft, P., and Steinhorn, C., Between groups and rings, The Rocky Mountain Journal of Mathematics, vol. 19 (1989), no. 3, pp. 871–885.CrossRefGoogle Scholar
[12]Pillay, A. and Steinhorn, C., Definable sets in ordered structures, I, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 565–592.CrossRefGoogle Scholar
[13]Poston, R., Defining multiplication in o-minimal expansions of the additive reals, this Journal, vol. 60 (1995), pp. 797–816.Google Scholar
[14]Remmert, R., Classical topics in complex function theory, Graduate Texts in Mathematics, vol. 172, Springer, 1998.CrossRefGoogle Scholar
[15]Strzebonski, A., One-dimensional groups definable in o-minimal structures, Journal of Pure and Applied Algebra, vol. 96 (1994), pp. 203–214.CrossRefGoogle Scholar
[16]van den Dries, L., Remarks on Tarski's problem concerning ⟨R, +, ·, exp⟩, Logic colloquium 1982, North-Holland, 1984, pp. 97–121.Google Scholar
[17]van den Dries, L., A generalization of the Tarski-Seidenberg theorem, and some nondefinability results, Bulletin of the American Mathematical Society, vol. 15 (1986), pp. 189–193.CrossRefGoogle Scholar
[18]Wilkie, A. J., An algebraically conservative function, 1998, Paris 7 preprints Number 66.Google Scholar