Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T05:13:02.561Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic probabilities for second-order existential Kahr-Moore-Wang sentences

Published online by Cambridge University Press:  12 March 2014

Anne Vedø
Anne Vedø*
Affiliation:
Bølerlia 72, 0689 Oslo, Norway. E-mail: ave@ssb.no
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the 0-1 law does not hold for the class (∀∃∀ without = ) by finding a sentence in this class which almost surely expresses parity. We also show that every recursive real in the unit interval is the asymptotic probability of a sentence in this class. This expands a result by Lidia Tendera, who in 1994 proved that every rational number in the unit interval is the asymptotic probability of a sentence in the class ∀∃∀ with equality.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 304 - 319
Copyright
Copyright © Association for Symbolic Logic 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Aanderaa, S. O., On the decision problem for formulas in which all disjunctions are binary, Proceedings of the Second Scandinavian Logic Symposium, North-Holland, 1970.Google Scholar
[2]Compton, K. J., 0-1 laws in logic and combinatorics, NATO advanced study institute on algorithms and order, 1988, pp. 353–383.Google Scholar
[3]Dreben, D. and Goldfarb, W. D., The decision problem: Solvable classes of quantificational formulas, Addison-Wesley, 1979.Google Scholar
[4]Fagin, R., Probabilities on finite models, this Journal, vol. 41 (1976), pp. 50–58.Google Scholar
[5]Goldfarb, W. D., The Gödel class with equality is unsolvable, Bulletin of the American Mathematical Society, vol. 10 (1984), pp. 113–115.CrossRefGoogle Scholar
[6]Gurevich, Y., The decision problem for standard classes, this Journal, vol. 41 (1976), pp. 460–464.Google Scholar
[7]Kaufmann, M. and Shelah, S., On random models of finite power and monadic logic, Discrete Mathematics, vol. 54 (1985), pp. 285–293.CrossRefGoogle Scholar
[8]Kolaitis, P. G. and Vardi, M. Y., The decision problem for the probabilities of higher-order properties, Proceedings 19th ACM Symposium on Theory of Computing, 1987, pp. 425–435.Google Scholar
[9]Kolaitis, P. G., 0-1 laws and decision problems for fragments of second-order logic, Information and Computation, vol. 87 (1990), pp. 302–338.CrossRefGoogle Scholar
[10]Kolaitis, P. G., 0-1 laws for fragments of second-order logic: An overview, Logic from Computer Science (1992), pp. 265–286.CrossRefGoogle Scholar
[11]Kolaitis, P. G., Infinitary logics and0-1 laws, Information and Computation, vol. 98 (1992), pp. 258–294.CrossRefGoogle Scholar
[12]Lewis, H. R., Unsolvable classes of quantificational formulas, Addison-Wesley, 1979.Google Scholar
[13]Minsky, M. L., Computation: Finite and infinite machines, Prentice-Hall, 1967.Google Scholar
[14]Pacholski, L. and Szwast, W., The 0-1 law fails for the class of existential second-order Gödel sentences with eqality, Proceedings 30th IEEE Symposium on Foundations of Computer Science, 1989, pp. 160–163.CrossRefGoogle Scholar
[15]Pacholski, L., Asymptotic probabilities of existential second-order Gödel sentences, this Journal, vol. 56 (1991), pp. 427–438.Google Scholar
[16]Pacholski, L., On the 0-1 law for the class of existential second-order minimal Gödel sentences with equality, Proceedings 6th IEEE Symposium on Logic in Computer Science, 1991, pp. 280–285.Google Scholar
[17]Riordan, J., Combinatorial identities, Wiley, 1968.Google Scholar
[18]Tendera, L., A note on asymptotic probabilities of existential second-order minimal classes—the last step, Fundamenta Informaticae, vol. 20 (1994), pp. 277–285.CrossRefGoogle Scholar