Rizos Sklinos


Stevens Institute of Technology


Monday, April 5, 2021 - 4:00pm to 5:30pm

After Sela and Kharlampovich-Myasnikov proved that nonabelian free groups share the same common theory, a model theoretic interest for the theory of the free group arose. Moreover, maybe surprisingly, Sela proved that this common theory is stable. Stability is the first dividing line in Shelah's classification theory and it is equivalent to the existence of a nicely behaved independence relation - forking independence. This relation, in the theory of the free group, has been proved (Ould Houcine-Tent and Sklinos) to be as complicated as possible (n-ample for all n). This behavior of forking independence is usually witnessed by the existence of an infinite field. We prove that no infinite field is interpretable in the theory of the free group, giving the first example of a stable group which is ample but does not interpret an infinite field.