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Lovely pairs of models: the non first order case

  • Itay Ben-Yaacov (a1)
Abstract.

We prove that for every simple theory T (or even simple thick compact abstract theory) there is a (unique) compact abstract theory whose saturated models are the lovely pairs of T. Independence-theoretic results that were proved in [5] when is a first order theory are proved for the general case: in particular is simple and we characterise independence.

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[1]Ben-Yaacov, Itay, Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 85118.
[2]Ben-Yaacov, Itay, Simplicity in compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 163191.
[3]Ben-Yaacov, Itay, Thickness, and a categoric view of type-space functors, Fundamenta Mathematical, vol. 179 (2003), pp. 199224.
[4]Ben-Yaacov, Itay, Uncountable dense categoricity in cats, preprint.
[5]Ben-Yaacov, Itay, Pillay, Anand, and Vassiliev, Evgueni, Lovely pairs of models, Annals of Pure and Aplied Logic, vol. 122 (2003), pp. 235261.
[6]Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), pp. 293309.
[7]Kim, Byunghan, Forking in simple unstable theories, Journal of the London Mathematical Society, vol. 57 (1998), no. 2, pp. 257267.
[8]Kim, Byunghan and Pillay, Anand, Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 149164.
[9]Pillay, Anand, Forking in the category of existentially closed structures, Connections between Model Theory and Algebraic and Analytic Geometry (Macintyre, Angus, editor), Quaderni di Matematica, vol. 6, University of Naples, 2000.
[10]Poizat, Bruno, Paires de structures stables, this Journal, vol. 48 (1983), no. 2, pp. 239249.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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