Modelling with Integer Variables.

We give several results which characterize MIP-representability of sets and functions, and the finite union of MIP-representable sets. These results extend earlier ones due to R.R. Meyer. We provide representations whose linear relaxations have an efficient formulation, while retaining maximum accuracy to the problem modelled. Under mild hypotheses, these properties are retained as integer variables are set to values in nodes of branch-and-bound trees.