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Paper   IPM / M / 16959
School of Mathematics
  Title:   Dividing lines in unstable theories and subclasses of Baire 1 functions
  Author(s):  Karim Khanaki
  Status:   To Appear
  Journal: Arch. Math. Logic
  Supported by:  IPM
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 the first order theories.

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