Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-19T00:52:32.926Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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, 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