Submission date: 12 February 2023

Abstract:

In this paper we consider the classes of all continuous L-(pre-)structures for a continuous first-order signature L. We characterize the moduli of continuity for which the classes of finite, countable, or all continuous L-(pre-)structures have the amalgamation property. We also characterize when Urysohn continuous L-(pre)-structures exist, establish that certain classes of finite continuous L-structures are countable Fraïssé classes, prove the coherent EPPA for these classes of finite continuous L-structures, and show that actions by automorphisms on finite L-structures also form a Fraïssé class. As consequences, we have that the automorphism group of the Urysohn continuous L-structure is a universal Polish group and that Hall's universal locally finite group is contained in the automorphism group of the Urysohn continuous L-structure as a dense subgroup.

Mathematics Subject Classification: 03C66, 03C52, 03B60

Keywords and phrases:

Full text arXiv 2302.05867: pdf, ps.