Tameness in generalized metric structures
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Archive for Mathematical Logic |
| MU Faculty or unit | |
| 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. |
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