FORKING AND SUPERSTABILITY IN TAME AECS

SEBASTIEN VASEY
2016 Journal of Symbolic Logic (JSL)  
We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ZFC. We show that we already obtain a well-behaved independence relation assuming only a superstability-like hypothesis instead of categoricity. These methods are applied to obtain an upward stability transfer theorem from categoricity and
more » ... as well as new conditions for uniqueness of limit models.
doi:10.1017/jsl.2015.51 fatcat:ilt6o6wxx5ezdj223mwtijkmg4