Model theoretic stability and categoricity for complete metric spaces

Saharon Shelah, Alexander Usvyatsov

Research output: Contribution to journalArticlepeer-review


We deal with the systematic development of stability in the context of approximate elementary submodels of a monster metric space, which is not far, but still very different from first order model theory. In particular, we prove the analogue of Morley's theorem for classes of complete metric spaces.

Original languageEnglish
Pages (from-to)157-198
Number of pages42
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Mar 2011
Externally publishedYes

Bibliographical note

Funding Information:
∗ We would like to thank Alice Leonhardt for the beautiful typing. Research partially supported by National Science Foundation Grants No. NSF-DMS 0100794 and 0600940. We thank the anonymous referee for very helpful comments and suggestions which greatly improved the exposition, especially in the last section of the paper. ∗∗The first author would like to thank the Israel Science Foundation for partial support of this research (Grant No. 242/03). Publication 837. Received January 2, 2007 and in revised form June 10, 2009


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