On classification of continuous first order theories
Abstract
We give several new characterizations of (the independence property) and (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 or , for real-valued logics, especially for continuous logic.
Cite
@article{arxiv.2205.12051,
title = {On classification of continuous first order theories},
author = {Karim Khanaki},
journal= {arXiv preprint arXiv:2205.12051},
year = {2026}
}
Comments
44 pages. Final version to appear in APAL. The paper was written in early 2019. It was first rejected by a journal for lacking sufficient significance for its scope. A second submission was later withdrawn after a very long delay due to the absence of any referee report, despite the editor's repeated efforts