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Preprint Number 2219

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2219. Ori Segel
Positive Definability Patterns

Submission date: 25 July 2022

! Abstract:

We reformulate Hrushovski's definability patterns from the setting of first order logic to the setting of positive logic. Given an h-universal theory T we put two structures on the type spaces of models of T in two languages, L and L_π. It turns out that for sufficiently saturated models, the corresponding h-universal theories T and T_π are independent of the model. We show that there is a canonical model J of T, and in many interesting cases there is an analogous canonical model J_π of T_π, both of which embed into every type space. We discuss the properties of these canonical models, called cores, and give some concrete examples.

Mathematics Subject Classification: 03C95

Keywords and phrases:

Full text arXiv 2207.12449: pdf, ps.

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