Counting finite models

Journal of Symbolic Logic

Volumn 62, Issue 3, 1997, Pages 925-949

  Woods, Alan R ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031517108     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2307/2275580     Document Type: Article

References (46)

1. E. A. BENDER, Asymptotic methods in enumeration, SIAM Review, vol. 16 (1974), pp. 485-515.
2. A. BLASS, Y. GUREVICH, and D. KHZEN, A zero-one law for logic with a fixed point operator, Information and Control, vol. 67 (1985), pp. 70-90.
3. K. J. COMPTON, Application of a Tauberian theorem to finite model theory, Arch. Math. Logik Grundlag, vol. 25 (1985), pp. 91-98.
4. _, A logical approach to asymptotic combinatorics I: first order properties. Advances in Mathematics, vol. 65 (1987), pp. 65-96.
5. _, Some methods for computing component distribution probabilities in relational structures. Discrete Mathematics, vol. 66 (1987), pp. 59-77.
6. _, A logical approach to asymptotic combinatorics II: monadic second-order properties. Journal of Combinatorial Theory. Series A, vol. 50 (1989), pp. 110-131.
7. K. J. COMPTON, C. W. HENSON, and S. SHELAH, Nonconvergence, undecidability, and intractability in asymptotic problems. Annals of Pure and Applied Logic, vol. 36 (1987), pp. 207-224.
8. H.-D. EBBINGHAUS and J. FLUM. Finite model theory, Springer-Verlag, Berlin, 1995.
9. A. EHRENFEUCHT, An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, vol. 49 (1961), pp. 129-141.
10. R. FAGIN, Probabilities on finite models, this JOURNAL, vol. 41 (1976), pp. 50-58.
11. W. FELLER, Introduction to probability theory and its applications, vol. 2, Wiley, New York, 1971.
12. R. A. FISHER, Some combinatorial theorems and enumerations connected with the numbers of diagonal types of a latin square, Annals of Eugenics, vol. 11 (1942), pp. 395-401.
13. _, Collected papers of R. A. Fisher (J. H. Bennett, editor), University of Adelaide, 1974.
14. J. FOY and A. WOODS, Asymptotic number of nonisomorphic finite models with function symbols (preliminary report). Abstracts of the American Mathematical Society, vol. 843-03-85 (1988), p. 238.
15. J. FOY and A. R. WOODS, Probabilities of sentences about two linear ordering, Feasible mathematics, A Mathematical Sciences Institute Workshop, Ithaca, New York, June 1989 (S. R. Buss and P. J. Scott, editors), Birkhäuser, Boston, 1990, pp. 181-193.
16. J. M. FOY, Probability and enumeration results in the theory of finite models, Ph.D. thesis, Yale University, New Haven CT, 1994.
17. R. FRAÏSSÉ, Sur quelques classifications des systèmes de relations. Pub. Sci. Univ. Alger. Ser. A., vol. 1 (1954), pp. 35-182.
18. R. FREESE, On the two kinds of probability in algebra, Algebra Universalis, vol. 27 (1990), pp. 70-79.
19. Y. V. GLEBSKIǏ, D. I. KOGAN, M. I. LIOGON'KIǏ, and V. A. TALANOV, Range and degree of realizability of formulas in the restricted predicate calculus, Kibernetika (Kiev), vol. 5 (1969). no. 2, pp. 17-28, English translation Cybernetics, vol. 5 (1972), pp. 142-154.
20. Y. V. GLEBSKIǏ, D. I. KOGAN, M. I. LIOGON'KIǏ, and V. A. TALANOV, Range and degree of realizability of formulas in the restricted predicate calculus, Kibernetika (Kiev), vol. 5 (1969). no. 2, pp. 17-28, English translation Cybernetics, vol. 5 (1972), pp. 142-154.
21. I. P. GOULDEN and D. M. JACKSON, Combinatorial enumeration, Wiley, New York, 1983.
22. Y. GUREVICH, Monadic second-order theories, Model-theoretic logics (J. Barwise and S. Feferman, editors), Springer-Verlag, New York, 1985, pp. 479-506.
23. F. HARARY, The number of functional digraphs, Mathematische Annalen, vol. 138 (1959), pp. 203-210.
24. F. HARARY and E. M. PALMER, Graphical enumeration, Academic Press, New York, 1973.
25. L. KATZ, Probability of indecomposability of a random mapping function, Annals of Mathematical Statistics, vol. 26 (1955), pp. 512-517.
26. M. KAUFMANN and S. SHELAH, On random models of finite power and monadic logic, Discrete Mathematics, vol. 54 (1985), pp. 285-293.
27. J. F. LYNCH, Probabilities of first-order sentences about unary functions, Transactions of the American Mathematical Society, vol. 287 (1985), pp. 543-568.
28. _, Convergence laws for random words, Australian Journal of Combinatorics, vol. 7 (1993), pp. 145-156.
29. _, An extension of 0-1 laws, Random Structures Algorithms, vol. 5 (1994), pp. 155-172.
30. A. MEIR and J. W. MOON, On random mapping patterns, Combinatorica, vol. 4 (1984), pp. 61-70.
31. _, Some asymptotic results useful in enumeration problems, Aequationes Mathematicae, vol. 33(1987), pp. 260-268.
32. J. W. MOON, Counting labelled trees, Canadian Mathematical Monographs, vol. 1, Canadian Mathematical Congress, 1970.
33. R. OTTER, The number of trees, Annals of Mathematics, vol. 49 (1948), pp. 583-599.
34. G. PÓLYA, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Mathematica, vol. 68 (1937), pp. 145-254.
35. G. POLYA and R. C. READ, Combinatorial enumeration of groups, graphs, and chemical compounds, Springer-Verlag, New York, 1987.
36. R. C. READ, A note on the number of functional digraphs, Mathematische Annalen, vol. 143 (1961), pp. 109-110.
37. A. RÉNYI, On connected graphs, I, Publ. Math. Inst. Hung. Acad. Sci., vol. 4 (1959), pp. 385-388.
38. S. SHELAH, The monadic theory of order, Annals of Mathematics, vol. 102 (1975), pp. 379-419.
39. J. SPENCER, Nonconvergence in the theory of random orders, Order, vol. 7 (1990/91), pp. 341-348.
40. V. A. TALANOV and V. V. KNYAZEV, The asymptotic truth value of infinite formulas, Proceedings of the all-Union seminar on discrete mathematics and its applications (Moscow 1984), Moskov. Gos. Univ., Mekh. Mat. Fak., Moscow, 1986, in Russian, MR 89g:03054, pp. 56-61.
41. J. TYSZKIEWICZ, Infinitary queries and their asymptotic probabilities I: properties definable in transitive closure logic, Computer science logic, proc. 5th workshop, CSL'91 Berne Switzerland, October 1991 (E. Borger, G. Jäger, H. Klein Büning, . and M. M. Richter, editors), Lecture Notes in Computer Science, vol. 626, Springer-Verlag, 1992, pp. 396-410.
42. _, On asymptotic probabilities of monadic second order properties, Computer science logic, proc. 6th workshop, CSL'92 San Miniato, 1992 (E. Borger, G. Jäger, H. Klein Büning, S. Martini, and M. M. Richter, editors), Lecture Notes in Computer Science, vol. 702, Springer-Verlag, 1993, pp. 425-439.
43. _, Infinitary queries and their asymptotic probabilities. II. Properties definable in least fixed point logic, Random Structures Algorithms, vol. 5 (1994), pp. 215-234.
44. _, Probabilities in first-order logic of a unary function and a binary relation, Random Structures Algorithms, vol. 6 (1995), pp. 181-192.
45. H. S. WILF, generatingfunctionology, Academic Press, Boston, 1990.
46. A. R. WOODS, Colouring rules for finite trees, and probabilities of monadic second order sentences, Research Report 15, Department of Mathematics, University of Western Australia, 1995.