Tameness in generalized metric structures

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Authors	LIEBERMAN Michael ROSICKÝ Jiří ZAMBRANO Pedro
Year of publication	2023
Type	Article in Periodical
Magazine / Source	Archive for Mathematical Logic
MU Faculty or unit	Faculty of Science
Citation
Web	https://doi.org/10.1007/s00153-022-00852-4
Doi	http://dx.doi.org/10.1007/s00153-022-00852-4
Keywords	Abstract model theory; Metric abstract elementary classes; Metric structures; Quantales; Quantale-valued metrics; Tameness
Description	We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a proof of concept we show that the result of Boney and Zambrano (Around the set-theoretical consistency of d-tameness of metric abstract elementary classes, arXiv:1508.05529, 2015) 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.
Related projects:	Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku