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Stable models and reflexive banach spaces

Published online by Cambridge University Press:  12 March 2014

José Iovino
José Iovino*
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke str. west, Montréal, Québec, Canada, H31 2K6, E-mail: iovino@math.mcgill.caDepartment of Mathematical Sciences, Carnegie Mellon UniversityPittsburgh, PA 15213, USA
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Abstract

We show that a formula φ(x, y) is stable if and only if φ is the pairing map on the unit ball of E × E*, where E is a reflexive Banach space. The result remains true if the formula φ is replaced by a set of formulas .

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999, pp. 1595 - 1600
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Aldous, D. J., Subspaces of L1, via random measures, Transactions of the American Mathematical Society, vol. 2 (1981), no. 267, pp. 445–463.Google Scholar
[2]James, R. C., Uniformly non-square Banach spaces, Annals of Math. (1964), no. 80, pp. 542–550.Google Scholar
[3]Krivine, J.-L. and Maurey, B., Espaces de Banach stables, Israel Journal of Mathematics, vol. 4 (1981), no. 39, pp. 273–295.CrossRefGoogle Scholar
[4]Raynaud, Y., Espaces de Banach superstables, distances stables et homéomorphismes uniformes, Israel Journal of Mathematics (1983), no. 44, pp. 33–52.CrossRefGoogle Scholar
[5]Shelah, S., Classification theory and the number of nonisomorphic models, Studies in Logic and the Foundations of Mathematics, vol. 92, North-Holland Publishing Co., Amsterdam, second ed., 1990.Google Scholar