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RECONSTRUCTION OF SEPARABLY CATEGORICAL METRIC STRUCTURES

Published online by Cambridge University Press:  26 January 2016

ITAÏ BEN YAACOV
Affiliation:
UNIVERSITÉ CLAUDE BERNARD – LYON 1 INSTITUT CAMILLE JORDAN, CNRS UMR 5208 43 BOULEVARD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX FRANCEURL: http://math.univ-lyon1.fr/∼begnac/
ADRIANE KAÏCHOUH
Affiliation:
UNIVERSITÉ CLAUDE BERNARD – LYON 1 INSTITUT CAMILLE JORDAN, CNRS UMR 5208 43 BOULEVARD DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX FRANCEURL: http://math.univ-lyon1.fr/∼kaichouh/

Abstract

We extend Ahlbrandt and Ziegler’s reconstruction results ([1]) to the metric setting: we show that separably categorical structures are determined, up to bi-interpretability, by their automorphism groups.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

REFERENCES

Ahlbrandt, Gisela and Ziegler, Martin, Quasi-finitely axiomatizable totally categorical theories. Annals of Pure and Applied Logic, vol. 30 (1986), no. 1, pp. 6382.CrossRefGoogle Scholar
Yaacov, Itaï Ben, Definability of groups in0-stable metric structures, this Journal, vol. 75 (2010), no. 3, pp. 817840.Google Scholar
Yaacov, Itaï Ben, On theories of random variables. Israel Journal of Mathematics, vol. 194 (2013), no. 2, pp. 9571012.CrossRefGoogle Scholar
Yaacov, Itaï Ben, Berenstein, Alexander, Henson, C. Ward, and Usvyatsov, Alexander, Model theory for metric structures, Model Theory with Applications to Algebra and Analysis. Vol. 2, London Mathematical Society Lecture Note Series, vol. 350, Cambridge University Press, Cambridge, 2008, pp. 315427.Google Scholar
Yaacov, Itaï Ben and Tsankov, Todor, Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups, preprint.Google Scholar
Yaacov, Itaï Ben and Usvyatsov, Alexander, On d-finiteness in continuous structures. Fundamenta Mathematicae, vol. 194 (2007), pp. 6788.Google Scholar
Yaacov, Itaï Ben and Usvyatsov, Alexander, Continuous first order logic and local stability. Transactions of the American Mathematical Society, vol. 362 (2010), no. 10, pp. 52135259.Google Scholar
Ibarlucía, Tomás, The dynamical hierarchy for Roelcke precompact Polish groups, research notes.Google Scholar
Melleray, Julien, A note on Hjorth’s oscillation theorem, this Journal, vol. 75 (2010), no. 4, pp. 13591365.Google Scholar
Rosendal, Christian, A topological version of the Bergman property. Forum Mathematicum, vol. 21 (2009), no. 2, pp. 299332.Google Scholar