Tameness and frames revisited

We combine tameness for types of singleton with the existence of a good frame to obtain some amount of tameness for types of longer sequences. We use this to show how to use tameness to extend a good frame in one cardinality to a good frame in all cardinalities, improving a theorem of Boney. Along the way, we prove many general results on the independent sequences induced by the good frame. In particular, we show that tameness and a good frame imply Shelah's notion of dimension is well-behaved, complementing previous work of Jarden and Sitton.