Souslin Quasi-Orders and Bi-Embeddability of Uncountable Structures

Souslin Quasi-Orders and Bi-Embeddability of Uncountable Structures Synopsis

"We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case) for arbitrary -Souslin quasi-orders on any Polish space, for an infinite cardinal smaller than the cardinality of R. These generalizations yield a variety of results concerning the complexity of the embeddability relation between graphs or lattices of size , the isometric embeddability relation between complete metric spaces of density character , and the linear isometric embeddability relation between (real or complex) Banach spaces of density "--.