Abstract
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.
Publisher
Cambridge University Press (CUP)
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