Journal of Symbolic Logic

On supersimplicity and lovely pairs of cats

Itay Ben-Yaacov

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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.

Article information

Source
J. Symbolic Logic, Volume 71, Issue 3 (2006), 763-776.

Dates
First available in Project Euclid: 4 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1154698575

Digital Object Identifier
doi:10.2178/jsl/1154698575

Mathematical Reviews number (MathSciNet)
MR2250819

Zentralblatt MATH identifier
1109.03025

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48] 03C90: Nonclassical models (Boolean-valued, sheaf, etc.) 03C95: Abstract model theory

Keywords
beautiful pairs lovely pairs supersimplicity superstability Hausdorff cats metric structures

Citation

Ben-Yaacov, Itay. On supersimplicity and lovely pairs of cats. J. Symbolic Logic 71 (2006), no. 3, 763--776. doi:10.2178/jsl/1154698575. https://projecteuclid.org/euclid.jsl/1154698575


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References

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