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Abstract:

We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property κ_{cdt}(T), κ_{sct}(T), and κ_{inp}(T) and the relations that obtain between them. From strong colorings, we construct theories T with κ_{cdt}(T) > κ_{sct}(T) + κ_{inp}(T). We show that these invariants have distinct structural consequences, by investigating the decay of saturation in ultrapowers of models of T, where T is some theory with κ_{cdt}(T), κ_{sct}(T), or κ_{inp}(T) large and bounded. This answers some questions from [shelah1990classification].

Mathematics Subject Classification: 03C45, 03C55

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Full text arXiv 1511.06453: pdf, ps.