2019/04/30 by Karim Khanaki
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebra over a field #Baire category theorem #Baire measure #Baire space #Characterization (materials science) #Class (philosophy) #Computability, Logic, AI Algorithms #Discrete mathematics #Epistemology #Independence (probability theory) #Mathematical and Theoretical Analysis #Mathematics #Model theory #Order (exchange) #Property (philosophy) #Pure mathematics #math.LO #msc:03C45
paper · pdf · doi:10.1007/s00153-022-00816-8
In this new version there are minor corrections. (23 pages)
arxiv created 2022/02/16 · openalex publication_date 2022/03/09 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a new characterization of SOP (the strict order property) in terms of the behaviour of formulas in any model of the theory as opposed to having to look at the behaviour of indiscernible sequences inside saturated ones. We refine a theorem of Shelah, namely a theory has OP (the order property) if and only if it has IP (the independence property) or SOP, in several ways by characterizing various notions in functional analytic style. We point out some connections between dividing lines in first order theories and subclasses of Baire 1 functions, and give new characterizations of some classes and new classes of first order theories.