# Menachem Magidor: Omitting types in the logic of metric structures

HUJI Logic Seminar

16/Jan/2019, 11-13, Ross 63.

Speaker: Menachem Magidor

Title: Omitting types in the logic of metric structures

Abstract.

(joint work with I. Farah)

The logic of metric structures was introduced by Ben Yaacov, Berenstein , Henson and Usvyatsov. It is a version of continuous logic which allows fruitful model theory for many kinds of metric structures. There are many aspects of this logic which make it similar to first order logic, like compactness, a complete proof system, an omitting types theorem for complete types etc. But when one tries to generalize the omitting type criteria to general (non-complete) types the problem turns out to be essentially more difficult than the first order situation. For instance one can have two types (in a complete theory) that each one can be omitted, but they can not be omitted simultaneously.

In the beginning of the talk we shall give a brief survey of the logic of metric structures, so the talk should be accessible also the listeners who are not familiar with the logic of metric structures.

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