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 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Continuous first order logic and local stability

Author(s): Itaï Ben Yaacov; Alexander Usvyatsov
Journal: Trans. Amer. Math. Soc. 362 (2010), 5213-5259.
MSC (2000): Primary 03C90, 03C45
Posted: May 17, 2010
MathSciNet review: 2657678
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Abstract | References | Similar articles | Additional information

Abstract: We develop continuous first order logic, a variant of the logic described by Chang and Keisler (1966). We show that this logic has the same power of expression as the framework of open Hausdorff cats, and as such extends Henson's logic for Banach space structures. We conclude with the development of local stability, for which this logic is particularly well-suited.

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Itaï Ben Yaacov and Alexander Usvyatsov, On $ d$-finiteness in continuous structures, Fundamenta Mathematicæ 194 (2007), 67-88. MR 2291717 (2007m:03080)

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C. C. Chang and H. Jerome Keisler, Continuous model theory, Princeton University Press, 1966. MR 0231708 (38:36)

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Saharon Shelah and Alexander Usvyatsov, Model theoretic stability and categoricity for complete metric spaces, preprint.

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Additional Information:

Itaï Ben Yaacov
Affiliation: Université de Lyon, Université Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France

Alexander Usvyatsov
Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
Address at time of publication: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal

DOI: 10.1090/S0002-9947-10-04837-3
PII: S 0002-9947(10)04837-3
Keywords: Continuous logic, metric structures, stability, local stability
Received by editor(s): November 28, 2005
Received by editor(s) in revised form: October 18, 2007 and June 2, 2008
Posted: May 17, 2010
Additional Notes: The research of the first author was supported by NSF grant DMS-0500172
The authors would like to thank C. Ward Henson for stimulating discussions, and Sylvia Carlisle and Eric Owiesny for a careful reading of the manuscript
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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