  We study a set of theories built on a ranked sequence of antisymmetric tensor
fields in D dimensional space-time. These linear theories exhibit gauge
invariances that are analogous to the local gauge invariance of a massless
vector (Maxwell) field. By appropriate arrangements of pairs of sequentially
ranked interacting fields in each member of a series of action functionals, we
produce a sequence of corresponding Higgs mechanism generalizations. Therefore,
mass arises in one field of each pair at the expense of the independent
existence of the other. The length of the sequence is determined by D.
