Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T09:36:13.462Z Has data issue: false hasContentIssue false
  • English
  • Français

On rational limits of Shelah–Spencer graphs

Published online by Cambridge University Press:  12 March 2014

Justin Brody  and
M. C. Laskowski
Justin Brody
Affiliation:
Department of Mathematics and Computer Science, Franklin & Marshall College, Po Box 3003, Lancaster, PA 17604-3003, USA, E-mail: justin.brody@fandm.edu
M. C. Laskowski
Affiliation:
Department of Mathematics, Mathematics Building, University of Maryland, College Park, Md 20742-4015, USA, E-mail: mcl@math.umd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Given a sequence {αn} 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 580 - 592
Copyright
Copyright © Association for Symbolic Logic 2012

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] Baldwin, John T. and Shelah, Saharon, Randomness and semigenerieity. Transactions of the American Mathematical Society, vol. 349 (1997), no. 4, pp. 1359–1376.CrossRefGoogle Scholar
[2] Baldwin, John T. and Shelah, Saharon, DOP and FCP in generic structures, this Journal, vol. 63 (1998), pp. 427–438.Google Scholar
[3] Baldwin, John T. and Shi, Niandong, Stable generic structures, Annals of Pure and Applied Logic, vol. 79 (1996), no. 1, pp. 1–35.CrossRefGoogle Scholar
[4] Ikeda, Koichiro, Kikyo, Hirotaka, and Tsuboi, Akito. On generic structures with a strong amalgamation property, this Journal, vol. 74 (2009), no. 3, pp. 721–733.Google Scholar
[5] Laskowski, Michael C., A simpler axiomatization of the Shelah–Spencer almost sure theories, Israel Journal of Mathematics, vol. 161 (2007), pp. 157–186.CrossRefGoogle Scholar
[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. 97–115.CrossRefGoogle Scholar
[7] Spencer, Joel, The strange logic of random graphs. Algorithms and Combinatorics, vol. 22. Springer-Verlag, Berlin, 2001.CrossRefGoogle Scholar
[8] Tarski, Alfred, Mostowski, A., and Robinson, R. M.. Undecidable theories, North-Holland, 1968.Google Scholar
[9] Wagner, Frank O., Relational structures and dimensions. Automorphisms of first-order structures, Oxford Science Publications, Oxford University Press, New York, 1994, pp. 153–180.CrossRefGoogle Scholar