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Non-genericity phenomena in ordered Fraïssé classes

Published online by Cambridge University Press:  12 March 2014

Konstantin Slutsky
Konstantin Slutsky*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA, E-mail: kslutsky@gmail.com
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Abstract

We show that every two-dimensional class of topological similarity, and hence every diagonal conjugacy class of pairs, is meager in the group of order preserving bijections of the rationale and in the group of automorphisms of the ordered rational Urysohn space.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 3 , September 2012 , pp. 987 - 1010
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1] Hodges, W., Model theory, Cambridge Univ. Press., 1993.Google Scholar
[2] Kechris, A. S., Pestov, V. G., and Todorcevic, S., Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups, Geometric and Functional Analysis, vol. 15 (2005), no. 1, pp. 106–189.CrossRefGoogle Scholar
[3] Kechris, A.S. and Rosendal, C., Turbulence, amalgamation and generic automorphisms of homogeneous structures, Proceedings of the London Mathematical Society, vol. 94 (2007), pp. 349–371.CrossRefGoogle Scholar
[4] Melleray, J., Topology of the isometry group of the urysohn space, Fundamenta Mathematicae, vol. 207 (2010), no. 3, pp. 273–287.CrossRefGoogle Scholar
[5] Rosendal, C., The generic isometry and measure preserving homeomorphism are conjugate to their powers, Fundamenta Mathematicae, vol. 205 (2009), no. 1, pp. 1–27.CrossRefGoogle Scholar
[6] Solecki, S., Extending partial isometrics, Israel Journal of Mathematics, vol. 150 (2005), pp. 315–332.CrossRefGoogle Scholar
[7] Truss, J. K., On notions of genericity and mutual genericity, this Journal, vol. 72 (2007), pp. 755–766.Google Scholar