Separation principles in the hierarchy theory of pure first-order logic
M. R. Krom · Journal of Symbolic Logic · 1963
This paper answers negatively the chief remaining open questions concerning the separation properties of first-order prefix classes of structures (discussed by Addison [2], pp. 26–37). 1. Preliminaries. The first and second separation properties and the reduction property are defined for arbitrary classes of subsets of an arbitrary set.