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Probabilities on models of universal sentences

Author: Douglas N. Hoover
Journal: Proc. Amer. Math. Soc. 98 (1986), 294-297
MSC: Primary 03C13; Secondary 68Q15
MathSciNet review: 854036
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Abstract: We show that the asymptotics of conditional probabilities of first order universal sentences on finite models are the same as those of general first order sentences. This answers a question of R. Fagin.

References [Enhancements On Off] (What's this?)

  • [1] Ronald Fagin, Generalized first-order spectra and polynomial-time recognizable sets, Complexity of computation (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1973) Amer. Math. Soc., Providence, R.I., 1974, pp. 43–73. SIAM-AMS Proc., Vol. VII. MR 0371622
  • [2] Ronald Fagin, Probabilities on finite models, J. Symbolic Logic 41 (1976), no. 1, 50–58. MR 0476480,
  • [3] Y. V. Glebskii, D. I. Kogan, M. I. Liogon'kii, and V. A. Talanov, Range and degree of realizability of formulas in the restricted predicate calculus, Kybernetika (Prague) 5 (1969), 142-154.
  • [4] N. D. Jones and A. L. Selman, Turing machines and the spectra of first order formulas with equality, Proc. 4th ACM Sympos. on Theory of Computing, 1972, pp. 157-167.

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Keywords: Probabilities on finite models, conditional probabilities, finite spectra
Article copyright: © Copyright 1986 American Mathematical Society

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