“School of Mathematics”
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Paper IPM / M / 16959  


Abstract:  
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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