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On rational limits of Shelah–Spencer graphs

  • Justin Brody (a1) and M. C. Laskowski (a2)

Abstract

Given a sequence {α n } in (0,1) converging to a rational, we examine the model theoretic properties of structures obtained as limits of Shelah-Spencer graphs G(). We show that in most cases the model theory is either extremely well-behaved or extremely wild, and characterize when each occurs.

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References

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[1] Baldwin, John T. and Shelah, Saharon, Randomness and semigenerieity. Transactions of the American Mathematical Society, vol. 349 (1997), no. 4, pp. 13591376.
[2] Baldwin, John T. and Shelah, Saharon, DOP and FCP in generic structures, this Journal, vol. 63 (1998), pp. 427438.
[3] Baldwin, John T. and Shi, Niandong, Stable generic structures, Annals of Pure and Applied Logic, vol. 79 (1996), no. 1, pp. 135.
[4] Ikeda, Koichiro, Kikyo, Hirotaka, and Tsuboi, Akito. On generic structures with a strong amalgamation property, this Journal, vol. 74 (2009), no. 3, pp. 721733.
[5] Laskowski, Michael C., A simpler axiomatization of the Shelah–Spencer almost sure theories, Israel Journal of Mathematics, vol. 161 (2007), pp. 157186.
[6] Shelah, Saharon and Spencer, Joel. Zero-one laws for sparse random graphs. Journal of the American Mathematical Society, vol. 1 (1988), no. 1, pp. 97115.
[7] Spencer, Joel, The strange logic of random graphs. Algorithms and Combinatorics, vol. 22. Springer-Verlag, Berlin, 2001.
[8] Tarski, Alfred, Mostowski, A., and Robinson, R. M.. Undecidable theories, North-Holland, 1968.
[9] Wagner, Frank O., Relational structures and dimensions. Automorphisms of first-order structures, Oxford Science Publications, Oxford University Press, New York, 1994, pp. 153180.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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