On a generalized Fra\"iss\'e limit construction

In this paper, we present a slightly modified version of Fra"iss'e theory which is used in a paper by Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, Vladyslav Kalashnyk and Martino Lupini (arXiv:1411.4066) and another by the author (arXiv:1602.00124). Using this version, we also show that every UHF algebra can be recognized as a Fra"iss'e limit of a class of C*-algebras of matrix-valued continuous functions on cubes with distinguished traces.