We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the me tric to take values in a well-behaved quantale. As a proof of concept we show that the result of [BZ15] on...
moreWe broaden the framework of metric abstract elementary classes
(mAECs) in several essential ways, chiefly by allowing the me
tric to take values in a well-behaved quantale. As a proof of concept we show that the result of [BZ15] on (metric) tameness under a large cardinal assumption holds in this more general context. We briefly consider a further generalization to partial metric spaces, and hint at connections to classes of fuzzy structures, and structures on sheaves.
