On Urzyczyn's unoids with a connected underlying set

One of the most important properties characterizing the work of a program in an algebraic system is the truth-table property. This work is devoted to the study of some truth-table unoids. The beginning of these studies was initiated by works of P. Urzyczyn, in which sufficient truth-table conditions were proposed. However, the only truth-table unoid known by P.Urzyczyn was the union of an infinite number of pairwise disjoint unoids, each of which is isomorphic to the natural numbers together with the operation of follow. In this work the existence of a truth-table unoid with a connected underlying set is proved, thus showing that the requirement of disjointedness of the underlying set of an unoid is not essential.