Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T22:34:58.981Z Has data issue: false hasContentIssue false

The Morley rank of a Banach space

Published online by Cambridge University Press:  12 March 2014

José Iovino*
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA 15213, USA, E-mail: [email protected]

Abstract

We introduce the concepts of Morley rank and Morley degree for structures based on Banach spaces. We characterize ω-stability in terms of Morley rank, and prove the existence of prime models for ω-stable theories.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1996

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]Garling, D. H. J., Stable Banach spaces, random measures and Orlicz functions, Probability measures on groups, Lecture Notes in Mathematics, vol. 928, Springer-Verlag, Berlin–New York, 1982.CrossRefGoogle Scholar
[2]Heinrich, S. and Henson, C. W., Banach space model theory II: Isomorphic equivalence, Mathematische Nachrichten, vol. 125 (1986), pp. 301317.CrossRefGoogle Scholar
[3]Henson, C. W., Banach space model theory III: Separable spaces under isometric equivalence, in preparation.Google Scholar
[4]Henson, C. W., Some examples of stable Banach spaces, in preparation.Google Scholar
[5]Henson, C. W. and Iovino, J., Banach space model theory I: Basics, in preparation.Google Scholar
[6]Iovino, J., Stable Banach spaces I: Fundamentals, submitted.Google Scholar
[7]Kelley, J., General topology, Van Nostrand, Princeton, 1955.Google Scholar
[8]Raynaud, Y., Séparabilité uniforme de L'espace des types d'un espace de Banach—Quelques exemples, Séminaire de Geometrie des espaces de Banach, Université Paris 7, vol. 2 (1983).Google Scholar