Work

The Amalgamation Property and Urysohn Structures in Continuous Logic

Year: 2024

Type: article

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

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2024.26

Authors: SU GAO, XUANZHI REN

Institution: Nankai University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: National Natural Science Foundation of China