A (one-sided) sequence or (two-sided) bisequence is irreducible provided it contains no block of the form BBb, where b is the initial symbol of the block B. Gottschalk and Hedlund [Proc. Amer. Math. Soc. 15 (1964), 70-74] proved that the set of irreducible binary bisequences is the Morse minimal set M. Let M+ denote the one-sided Morse minimal set, i.e. M+ -{x0xxx2 . . . : . .. x_xx0xx . . . e A/}. Let P + denote the set of all irreducible binary sequences. We establish a method for generating

more »

... ll x e P +. We also determine P + -M +. Considering P + as a one-sided symbolic flow, P + is not the countable union of transitive flows, thus P+ is considerably larger than M+. However M+ is the u-limit set of each x e P +, and in particular M * is the nonwandering set of P +.