We introduce the notions of copyable and diagonalizable classes of structures. We then show how these notions are connected to two other notions that had already been studied for some particular classes of structures, namely the listability property and the low property.
The main result of this paper is the characterizations of the classes of structures with the low property, that is, the classes whose low members all have computable copies. We characterize these classes as the ones whose structural jumps are listable.
"Copyable structures." J. Symbolic Logic 78 (4) 1199 - 1217, December 2013. https://doi.org/10.2178/jsl.7804110