  The main object of this work is to present a powerful method of construction
of subshifts which we use chiefly to construct WAP systems with various
properties. Among many other applications of this so called labeled subshifts,
we obtain examples of null as well as non-null WAP subshifts, WAP subshifts of
arbitrary countable (Birkhoff) height, and completely scrambled WAP systems of
arbitrary countable height. We also construct LE but not HAE subshifts, and
recurrent non-tame subshifts.

Dynamical Systems