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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotics for logical limit laws: When the growth of the components is in an RT class


Authors: Jason P. Bell and Stanley N. Burris
Journal: Trans. Amer. Math. Soc. 355 (2003), 3777-3794
MSC (2000): Primary 03C13, 05A16, 11P99, 41A60; Secondary 11N45, 11N80, 11U99, 60J20
Published electronically: May 29, 2003
MathSciNet review: 1990173
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Abstract | References | Similar Articles | Additional Information

Abstract: Compton's method of proving monadic second-order limit laws is based on analyzing the generating function of a class of finite structures. For applications of his deeper results we previously relied on asymptotics obtained using Cauchy's integral formula. In this paper we develop elementary techniques, based on a Tauberian theorem of Schur, that significantly extend the classes of structures for which we know that Compton's theory can be applied.


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Additional Information

Jason P. Bell
Affiliation: Mathematics Department, University of Michigan, East Hall, 525 East University, Ann Arbor, Michigan 48109-1109
Email: belljp@umich.edu

Stanley N. Burris
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada
Email: snburris@thoralf.uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03299-9
PII: S 0002-9947(03)03299-9
Keywords: Ratio test, Schur's Tauberian theorem, asymptotic density, monadic second-order logic, zero-one law, limit law
Received by editor(s): June 26, 2002
Received by editor(s) in revised form: January 10, 2003
Published electronically: May 29, 2003
Additional Notes: The second author would like to thank NSERC for support of this research
Article copyright: © Copyright 2003 American Mathematical Society