# Logic Seminar - Rosario Mennuni (Pisa)

Dates: | 4 May 2022 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Title: Automorphisms of ordered abelian groups and positive logic

Abstract: A common construction in model theory consists in starting with a theory T, adding to the language a symbol for an automorphism, resulting in a theory T', and looking at the class K of existentially closed models of T'. Sometimes, the class K is elementary; this is for example true when T is the theory of algebraically closed fields, where the corresponding theory of K is known as ACFA.

On the other hand, when T is a theory with SOP, by a result of Kikyo and Shelah the class K is not elementary. Nevertheless, positive logic allows to apply model theoretic techniques to the study of this class. In ongoing work of Jan Dobrowolski and myself, we look at the behaviour of NIP in this setting. For example, if T is the theory of dense linear orders, then the positive theory of K is NIP. We then look at the case where T is the theory of (divisible) ordered abelian groups.

In this talk, I will give a brief introduction to positive logic, review some existing results about generic automorphisms of ordered structures, and then report on ongoing work of Jan and myself about the class of divisible ordered abelian groups with an automorphism.