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On finite rigid structures

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich
Affiliation:
Department of EECS, University of Michigan, Ann Arbor, Michigan 48109, USA, E-mail: gurevich@umich.edu
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem 91904, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail: shelah@math.huji.ac.il
Corresponding

Abstract

The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no formula with counting quantifiers defines a linear order.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Dawar, Anuj, Feasible computation through model theory, Ph.D. thesis, Institute for Research in Cognitive Science University of Pennsylvania, Philadelphia, 1993.Google Scholar
[2]Gurevich, Yuri, Logic and the challenge of computer science, Current trends in theoretical computer science (Börger, E., editor), Computer Science Press, 1988, pp. 157.Google Scholar
[3]Immerman, Neil and Lander, E. S., Describing graphs: A first-order approach to graph canonization, Complexity theory retrospective (Selman, Alan, editor), Springer Verlag, 1990, pp. 5981.CrossRefGoogle Scholar
[4]Stolboushkin, Alexei, Axiomatizable classes of finite models and definability of linear order, Proceedings of the 7th IEEE Annual Symposium on Logic in Computer Science (1992), pp. 6470.Google Scholar
[5]Weinstein, Scott, private correspondence, 10 1993.Google Scholar

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