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Lovely pairs of models: the non first order case

Published online by Cambridge University Press:  12 March 2014

Itay Ben-Yaacov
Itay Ben-Yaacov*
Affiliation:
University of Wisconsin-Madison, Mathematics Department, 480 Lincoln DR, Madison WI 53706-1388, USA, E-mail: pezz@math.mit.edu, URL: http://www-math.mit.edu/~pezz
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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.

Keywords

simple theories – lovely pairs
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 641 - 662
Copyright
Copyright © Association for Symbolic Logic 2004

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References

REFERENCES

[1]Ben-Yaacov, Itay, Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 85–118.CrossRefGoogle Scholar
[2]Ben-Yaacov, Itay, Simplicity in compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 163–191.CrossRefGoogle Scholar
[3]Ben-Yaacov, Itay, Thickness, and a categoric view of type-space functors, Fundamenta Mathematical, vol. 179 (2003), pp. 199–224.CrossRefGoogle Scholar
[4]Ben-Yaacov, Itay, Uncountable dense categoricity in cats, preprint.Google Scholar
[5]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
[6]Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), pp. 293–309.Google Scholar
[7]Kim, Byunghan, Forking in simple unstable theories, Journal of the London Mathematical Society, vol. 57 (1998), no. 2, pp. 257–267.CrossRefGoogle Scholar
[8]Kim, Byunghan and Pillay, Anand, Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 149–164.CrossRefGoogle Scholar
[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.Google Scholar
[10]Poizat, Bruno, Paires de structures stables, this Journal, vol. 48 (1983), no. 2, pp. 239–249.Google Scholar