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

DOI:
https://doi.org/10.1090/S0002-9947-03-03299-9

Published electronically:
May 29, 2003

MathSciNet review:
1990173

Full-text PDF Free Access

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:
https://doi.org/10.1090/S0002-9947-03-03299-9

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