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
