Tameness in generalized metric structures

LIEBERMAN, Michael, Jiří ROSICKÝ and Pedro ZAMBRANO. Tameness in generalized metric structures. Archive for Mathematical Logic. Springer, 2023, vol. 62, 3-4, p. 531-558. ISSN 0933-5846. Available from: https://dx.doi.org/10.1007/s00153-022-00852-4.

Basic information

• Original name: Tameness in generalized metric structures
• Authors: LIEBERMAN, Michael (guarantor), Jiří ROSICKÝ (203 Czech Republic, belonging to the institution) and Pedro ZAMBRANO.
• Edition: Archive for Mathematical Logic, Springer, 2023, 0933-5846.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Germany
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.300 in 2022
• RIV identification code: RIV/00216224:14310/23:00134105
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1007/s00153-022-00852-4
• UT WoS: 000871171100001
• Keywords in English: Abstract model theory; Metric abstract elementary classes; Metric structures; Quantales; Quantale-valued metrics; Tameness
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

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.

Links

• GBP201/12/G028, research and development project: Name: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku

Investor: Czech Science Foundation