Information Security Seminar 

04/12/2009, 16:15 — 17:15 — Room P3.10, Mathematics Building
João Rasga, SQIG - IT / IST - TULisbon

A categorical view on quantifier-elimination - Part II

In the sequel of the talk of Cristina Sernadas we proceed by recognizing that, in some cases, a minimal model extending another can be obtained by iterating a certain construction, like for instance in the context of algebraically closed fields with the Artin's construction. We provide conditions that guarantee the existence of a $\omega$-limit functor identifying such an extension, when the theories are in ${\forall }_2$. The conditions are over the base functor and not the limit functor. The results are illustrated by showing that the theory of ACFs enjoy quantifier elimination. Joint work with Cristina Sernadas.