Notre Dame Journal of Formal Logic

The Field of LE-Series with a Nonstandard Analytic Structure

Ali Bleybel

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Abstract

In this paper we prove that the field of Logarithmic-Exponential power series endowed with the exponential function and a class of analytic functions containing both the overconvergent functions in the t-adic norm and the usual strictly convergent power series is o-minimal.

Article information

Source
Notre Dame J. Formal Logic Volume 52, Number 3 (2011), 255-265.

Dates
First available in Project Euclid: 28 July 2011

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1311875773

Digital Object Identifier
doi:10.1215/00294527-1435447

Mathematical Reviews number (MathSciNet)
MR2822488

Zentralblatt MATH identifier
05970093

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

Keywords
o-minimality exponential analytic structure

Citation

Bleybel, Ali. The Field of LE-Series with a Nonstandard Analytic Structure. Notre Dame J. Formal Logic 52 (2011), no. 3, 255--265. doi:10.1215/00294527-1435447. http://projecteuclid.org/euclid.ndjfl/1311875773.


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References

  • [1] Cluckers, R., L. Lipshitz, and Z. Robinson, "Real closed fields with non-standard and standard analytic structure", Journal of the London Mathematical Society. Second Series, vol. 78 (2008), pp. 198–212.
  • [2] van den Dries, L., A. Macintyre, and D. Marker, "The elementary theory of restricted analytic fields with exponentiation", Annals of Mathematics. Second Series, vol. 140 (1994), pp. 183–205.
  • [3] van den Dries, L., A. Macintyre, and D. Marker, "Logarithmic-exponential power series", Journal of the London Mathematical Society. Second Series, vol. 56 (1997), pp. 417–34.
  • [4] van den Dries, L., A. Macintyre, and D. Marker, "Logarithmic-exponential series", Annals of Pure and Applied Logic, vol. 111 (2001), pp. 61–113. Proceedings of the International Conference “Analyse & Logique” (Mons, 1997).
  • [5] van den Dries, L., and C. Miller, "On the real exponential field with restricted analytic functions", Israel Journal of Mathematics, vol. 85 (1994), pp. 19–56. Errata, vol. 92 (1995), p. 427.
  • [6] Fornasiero, A., and T. Servi, "Definably complete Baire structures", Fundamenta Mathematicae, vol. 209 (2010), pp. 215–41.
  • [7] Fratarcangeli, S., "A first-order version of Pfaffian closure", Fundamenta Mathematicae, vol. 198 (2008), pp. 229–54.
  • [8] Miller, C., "Expansions of dense linear orders with the intermediate value property", The Journal of Symbolic Logic, vol. 66 (2001), pp. 1783–90.
  • [9] Neumann, B. H., "On ordered division rings", Transactions of the American Mathematical Society, vol. 66 (1949), pp. 202–52.
  • [10] Sacks, G. E., Saturated Model Theory, Mathematics Lecture Note Series. W. A. Benjamin, Inc., Reading, 1972.