Tameness in generalized metric structures

• Autoři: LIEBERMAN Michael; ROSICKÝ Jiří; ZAMBRANO Pedro
• Rok publikování: 2023
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Archive for Mathematical Logic
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1007/s00153-022-00852-4
• Doi: http://dx.doi.org/10.1007/s00153-022-00852-4
• Klíčová slova: Abstract model theory; Metric abstract elementary classes; Metric structures; Quantales; Quantale-valued metrics; Tameness
• Popis: 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.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku