The field of reals with multisummable series and the exponential function

Proceedings of the London Mathematical Society

Volumn 81, Issue 3, 2000, Pages 513-565

  Van Den Dries, Lou ^a   Speissegger, Patrick ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012630722     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/s0024611500012648     Document Type: Article

References (25)

1. S. S. ABHYANKAR and T. T. MOH, 'A reduction theorem for divergent power series', J. Reine Angew. Math. 241 (1970) 27-33.
2. W. BALSER, From divergent power series to analytic functions, Lecture Notes in Mathematics 1582 (Springer, New York, 1994).
3. C. CHANG and H. KEISLER, Model theory (North-Holland, Amsterdam, 1973).
4. J. DENEF and L. VAN DEN DRIES, 'P-adic and real subanalytic sets', Ann. of Math. 128 (1988) 79-138.
5. L. VAN DEN DRIES, 'o-minimal structures', Logic: from foundations to applications (ed. W. Hodges et al., Oxford University Press, 1996).
6. L. VAN DEN DRIES, 'T-convexity and tame extensions II', J. Symbolic Logic 62 (1997) 14-34.
7. L. VAN DEN DRIES, Tame topology and o-minimal structures, London Mathematical Society Lecture Note Series 248 (Cambridge University Press, 1998).
8. L. VAN DEN DRIES and A. LEWENBERG, 'T-convexity and tame extensions', J. Symbolic Logic 60 (1995) 74-102.
9. L. VAN DEN DRIES, A. MACINTYRE and D. MARKER, 'The elementary theory of restricted analytic fields with exponentiation', Ann. of Math. 140 (1994) 183-205.
10. L. VAN DEN DRIES, A. MACINTYRE and D. MARKER, 'Logarithmic-exponential power series', J. London Math. Soc. (2) 56 (1997) 417-434.
11. L. VAN DEN DRIES and C. MILLER, 'On the real exponential field with restricted analytic functions', Israel J. Math. 85 (1994) 19-56.
12. L. VAN DEN DRIES and C. MILLER, 'Geometric categories and o-minimal structures', Duke Math. J. 84 (1996) 497-540.
13. L. VAN DEN DRIES and P. SPEISSEGGER, 'The real field with convergent generalized power series is model complete and o-minimal', Trans. Amer. Math. Soc. 350 (1998) 4377-4421.
14. A. GABRIELOV, 'Projections of semianalytic sets', Funct. Anal. Appl. 2 (1968) 282-291.
15. G. H. HARDY, Divergent series (Clarendon Press, Oxford, 1963).
16. J. MARTINET and J.-P. RAMIS, 'Elementary acceleration and multisummability I', Ann. Inst. Henri Poincaré 54 (1991) 331-401.
17. F. NEVANLINNA, 'Zur Theorie der asymptotischen Potenzreihen', Ann. Acad. Sci. Fenn. Math. XII (1919) 1-81.
18. N. NIELSEN, Die Gammafunktion (Chelsea, New York, 1965).
19. A. PRESTEL, Lectures on formally real fields, Lecture Notes in Mathematics 1093 (Springer, Berlin, 1984).
20. J.-P. RESSAYRE, 'Integer parts of real closed exponential fields', Arithmetic proof theory, and computational complexity (ed. P. Clote and J. Krajíček), Oxford Logic Guides 23 (Oxford University Press, New York, 1993) 278-288.
21. M. ROSENLIGHT, 'The rank of a Hardy field', Trans. Amer. Math. Soc. 280 (1983) 659-671.
22. J.-C. TOUGERON, 'Sur les ensembles semi-analytiques avec conditions Gevrey au bord', Ann. Sci. École Norm. Supl. (4) 27 (1994) 173-208.
23. E. WHITTAKER and G. WATSON, A course of modern analysis (Cambridge University Press, 1927).
24. A. J. WILKIE, 'A theorem of the complement and some new o-minimal structures', Selecta Math. (N.S.) 5 (1999) 397-421.
25. A. J. WILKIE, 'Model completeness results for expansions of the ordered field of real numbers by restricted pfaffian functions and the exponential function', J. Amer. Math. Soc. 9 (1996) 1051-1094.