Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-12T19:42:01.112Z Has data issue: false hasContentIssue false
  • English
  • Français

On supersimplicity and lovely pairs of cats

Published online by Cambridge University Press:  12 March 2014

Itay Ben-Yaacov
Itay Ben-Yaacov*
Affiliation:
University of Wisconsin – Madison, Department of Mathematics, 480 Lincoln Drive Madison, WI 53706, USAURL:http://www.math.wisc.edu/~pezz. E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that the definition of supersimplicity in metric structures from [7] is equivalent to an a priori stronger variant. This stronger variant is then used to prove that if T is a supersimple Hausdorff cat then so is its theory of lovely pairs.

Keywords

beautiful pairslovely pairssupersimplicitysuperstabilityHausdorff catsmetric structures
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 3 , September 2006 , pp. 763 - 776
Copyright
Copyright © Association for Symbolic Logic 2006

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]Ben-Yaacov, Itay, Discouraging results for ultraimaginary independence theory, this Journal, vol. 68 (2003), no. 3, pp. 846–850.Google Scholar
[2]Ben-Yaacov, Itay, Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 85–118.CrossRefGoogle Scholar
[3]Ben-Yaacov, Itay, Simplicity in compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 163–191.CrossRefGoogle Scholar
[4]Ben-Yaacov, Itay, Thickness, and a categoric view of type-space functors, Fundamenta Mathematicae, vol. 179 (2003), pp. 199–224.CrossRefGoogle Scholar
[5]Ben-Yaacov, Itay, Lovely pairs of models: the non first order case, this Journal, vol. 69 (2004), no. 3, pp. 641–662.Google Scholar
[6]Ben-Yaacov, Itay, Compactness and independence in non first order frameworks. The Bulletin of Symbolic Logic, vol. 11 (2005), no. 1, pp. 28–50.CrossRefGoogle Scholar
[7]Ben-Yaacov, Itay, Uncountable dense categoricity in cats, this Journal, vol. 70 (2005), no. 3, pp. 829–860.Google Scholar
[8]Ben-Yaacov, Itay, Schrödinger's cat, Israel Journal of Mathematics, to appear.Google Scholar
[9]Ben-Yaacov, Itay, Pillay, Anand, and Vassiliev, Evgueni, Lovely pairs of models, Annals of Pure and Aplied Logic, vol. 122 (2003), pp. 235–261.CrossRefGoogle Scholar
[10]Buechler, Steven, Pseudoprojective strongly minimal sets are locally projective, this Journal, vol. 56 (1991), no. 4, pp. 1184–1194.Google Scholar
[11]Buechler, Steven and Lessmann, Olivier, Simple homogeneous models, Journal of the American Mathematical Society, vol. 16 (2003), pp. 91–121.CrossRefGoogle Scholar
[12]Iovino, José, Stable Banach spaces and Banach space structures, I and II, Models, Algebras, and Proofs (BogotÁ, 1995), Lectures Notes in Pure and Applied Mathematics, no. 203, Dekker, New York, 1999, pp. 77–117.Google Scholar
[13]Poizat, Bruno, Paires de structures stables, this Journal, vol. 48 (1983), no. 2, pp. 239–249.Google Scholar
[14]Shelah, Saharon, The lazy model-theoretician's guide to stability, Logique et Analyse, vol. 71–72 (1975), pp. 241–308.Google Scholar
[15]Vassiliev, Evgueni, Generic pairs of SU-rank 1 structures, Annals of Pure and Applied Logic, vol. 120 (2002), pp. 103–149.CrossRefGoogle Scholar