Submission date: 24 May 2022

Abstract:

We give several new characterizations of IP (the independence property) and SOP (the strict order property) for continuous first order logic and study their relations to the function theory and the Banach space theory. We suggest new dividing lines of unstable theories by the study of subclasses of Baire-1 functions and argue why one should not expect a perfect analog of Shelah's theorem, namely a theory is unstable iff it has IP or SOP, for real-valued logics, especially for continuous logic.

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Full text arXiv 2205.12051: pdf, ps.