Uniqueness triples from the diamond axiom

Seminar
Speaker
Ari Brodsky (Ariel University)
Date
30/04/2018 - 15:00 - 13:00Add to Calendar 2018-04-30 13:00:00 2018-04-30 15:00:00 Uniqueness triples from the diamond axiom We work with a $\lambda$-frame, which is an abstract elementary class endowed with a collection of basic types and a non-forking relation satisfying certain natural properties with respect to models of cardinality $\lambda$. We will show that assuming the diamond axiom, any basic type admits a non-forking extension that has a uniqueness triple. Prior results of Shelah in this direction required either some form of diamond at two consecutive cardinals, or a constraint on the number of models of size $\lambda$. This is joint work of with Adi Jarden. Building 507, Room 204 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 507, Room 204
Abstract

We work with a $\lambda$-frame, which is an abstract elementary class endowed with a collection of basic types and a non-forking relation satisfying certain natural properties with respect to models of cardinality $\lambda$.

We will show that assuming the diamond axiom, any basic type admits a non-forking extension that has a uniqueness triple.
Prior results of Shelah in this direction required either some form of diamond at two consecutive cardinals, or a constraint on the number of models of size $\lambda$.

This is joint work of with Adi Jarden.

Last Updated Date : 13/04/2018