Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-09-17T20:51:38.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Expansions of geometries

Published online by Cambridge University Press:  12 March 2014

John T. Baldwin
John T. Baldwin*
Affiliation:
Department of Mathematics, Statistics and Computer Science, M/C 249, University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

For n < ω, expand the structure (n, S, I, F) (with S the successor relation, I, F as the initial and final element) by forming graphs with edge probability n−α for irrational α, with 0 < α < 1. The sentences in the expanded language, which have limit probability 1, form a complete and stable theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 3 , September 2003 , pp. 803 - 827
Copyright
Copyright © Association for Symbolic Logic 2003

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] Aref'ev, Roman, Baldwin, J. T., and Mazzucco, M., δ-invariant amalgamation classes, this Journal, vol. 64 (1999), pp. 1743–1750.Google Scholar
[2] Baldwin, J. T., Near model completeness and 0-1-laws, Proceedings of the DIMACS workshop on logic and random structures: 1995 (Boppana, R. and Lynch, James, editors), American Mathematical Society, 1997, pp. 1–13.Google Scholar
[3] Baldwin, J. T., Rank and homogeneous structures, Tits buildings and the theory of groups, Würzburg, Sept 14–17 2000 (Tent, Katrin, editor), Cambridge University Press, 2002.Google Scholar
[4] Baldwin, J. T., Random expansions of geometries, Original version on web: www.uic.edu/~jbaldwin.Google Scholar
[5] Baldwin, J. T. and Shelah, S., Randomness and semigenericity, Transactions of the American Mathematical Society, vol. 349 (1997), pp. 1359–1376.CrossRefGoogle Scholar
[6] Baldwin, J. T. and Shelah, S., DOP and FCP in generic structures, this Journal, vol. 63 (1998), pp. 427–439.Google Scholar
[7] Baldwin, J. T. and Shi, Niandong, Stable generic structures, Annals of Pure and Applied Logic, vol. 79 (1996), pp. 1–35.Google Scholar
[8] Bollobas, Béla, Extremal graph theory with emphasis on probabilistic methods, Conference Board of the Mathematical Sciences regional conference series, no. 62, American Mathematical Society, 1986.Google Scholar
[9] Hrushovski, E., Simplicity and the Lascar group, preprint.Google Scholar
[10] Hyttinen, T., Canonical finite diagrams and quantifier elimination, Mathematical Logic Quarterly, vol. 48 (2002), pp. 533–554.Google Scholar
[11] Lynch, J., Almost sure theories, Annals of Pure and Applied Logic, vol. 18 (1980), pp. 91–135.Google Scholar
[12] Lynch, J., Probabilities of sentences about very sparse random graphs, Random Structures and Algorithms, vol. 3 (1992), pp. 33–53.Google Scholar
[13] Pourmahdian, M., Simple generic theories, Ph.D. thesis , Oxford University, 2000.Google Scholar
[14] Rosen, E., Shelah, S., and Weinstein, S., κ-universal finite graphs, Proceedings of the DIMACS workshop on logic and random structures: 1995 (Boppana, R. and Lynch, James, editors), American Mathematical Society, 1996, pp. 65–77.Google Scholar
[15] Shelah, S., 0-1 laws, preprint 550, 200?Google Scholar
[16] Shelah, S., Zero-one laws with probability varying with decaying distance, Shelah 467, 200?Google Scholar
[17] Shelah, S. and Spencer, J., Zero-one laws for sparse random graphs, Journal of the American Mathematical Society, vol. 1 (1988), pp. 97–115.Google Scholar
[18] Spencer, J., Counting extensions, Journal of Combinatorial Theory A, vol. 55 (1990), pp. 247–255.Google Scholar
[19] Zil'ber, B. I., Uncountably categorical theories, Translations of the American Mathematical Society, American Mathematical Society, 1991.Google Scholar