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On finite rigid structures

  • Yuri Gurevich (a1) and Saharon Shelah (a2) (a3)


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.



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[1]Dawar, Anuj, Feasible computation through model theory, Ph.D. thesis, Institute for Research in Cognitive Science University of Pennsylvania, Philadelphia, 1993.
[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.
[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.
[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.
[5]Weinstein, Scott, private correspondence, 10 1993.


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