**Jouko Vaananen**will speak about some new infinitary logics.

**On some new infinitary logics**

__Abstract:__

Traditionally infinitary languages add to first order logic the capability of taking infinite conjunctions and disjunctions, and in a more expressive case universal and existential quantification over infinite strings of variables. As it turns out, the latter infinitary languages are systematically lacking in nice model theoretic properties, while the former ones permit some. In this talk we review an intermediate infinitary language introduced by Shelah in 2012 with a model-theoretic characterization and a potential for developing some model theory. This language is defined by describing what is required for recognising that two models are elementarily equivalent with respect to the language. The question has been raised whether there is a more traditional syntactically defined language with similar properties? In this talk we will introduce some alternatives and discuss their respective merits.

## Date:

Wed, 18/12/2019 - 11:00 to 13:00

## Location:

Ross building - Room 63