  Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be
a finite separable algebraic field extension with [L:F] = m. The integral
closure of V in L is a Dedekind domain that encodes the following invariants:
(i) the number of extensions of V to a valuation ring W on L, (ii) the residue
degree of each W over V, and (iii) the ramification degree of each W over V.
Given a finite set of DVRs on F, an m-consistent system is a family of sets
enumerating what is theoretically possible for the above invariants of each V
in the set. The m-consistent system is realizable if there exists a finite
separable extension field L/F that gives for each V the listed invariants. We
investigate the realizability of m-consistent systems.
