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Stability and stable groups in continuous logic

Published online by Cambridge University Press:  12 March 2014

Itaï Ben Yaacov
Itaï Ben Yaacov*
Affiliation:
Université Claude Bernard - Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 Boulevard Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France URL: http://math.univ-lyonl.fr/~begnac/
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Abstract

We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.

Keywords

stable theorycontinuous logicdefinable group
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 1111 - 1136
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

[Ben03a]Yaacov, Itaï Ben, Simplicity in compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 163–191.CrossRefGoogle Scholar
[Ben03b]Yaacov, Itaï Ben, Thickness, and a categoric view of type-space functors, Fundamenta Mathematicæ, vol. 179 (2003), pp. 199–224.CrossRefGoogle Scholar
[Ben05]Yaacov, Itaï Ben, Uncountable dense categoricity in cats, this Journal, vol. 70 (2005), no. 3, pp. 829–860.Google Scholar
[Ben06]Yaacov, Itaï Ben, On supersimplicity and lovely pairs of cats, this Journal, vol. 71 (2006), no. 3, pp. 763–776, arXiv: 0902.0118.Google Scholar
[Ben09]Yaacov, Itaï Ben, Modular functionals and perturbations of Nakano spaces, Journal of Logic and Analysis, vol. 1 (2009), no. 1, pp. 1–42, arXiv:0802.4285.Google Scholar
[Ben10]Yaacov, Itaï Ben, Definability of groups in Unstable metric structures, this Journal, vol. 75 (2010), no. 3, pp. 817–840.Google Scholar
[Ben]Yaacov, Itaï Ben, On theories of random variables, submitted, arXiv: 0901.1584.Google Scholar
[BU]Yaacov, Itaï Ben and Usvyatsov, Alexander, Continuous first order logic and local stability, Transactions of the American Mathematical Society, (to appear), arXiv: 0801.4303.Google Scholar
[Iov99]Iovino, José, Stable Banach spaces and Banach space structures, I and II, Models, algebras, and proofs (Bogotá, 1995), Lecture Notes in Pure and Applied Mathematics, vol. 203, Dekker, New York, 1999, pp. 77–117.Google Scholar
[Pil96]Pillay, Anand, Geometric stability theory, Oxford Logic Guides, vol. 32, The Clarendon Press Oxford University Press, New York, 1996, Oxford Science Publications.CrossRefGoogle Scholar
[Poi85]Poizat, Bruno, Cours de théorie des modéles, Nur al-Mantiq wal-Ma'rifah, 1985.Google Scholar