Modularity in the Semilattice of ω-Words

Abstract

A partial ordering ofω-words can be introduced with regard to whether anω-word can be transformed into another by a Mealy machine. It is known that the poset ofω-words that is introduced by this ordering is a join-semilattice. The width of this join-semilattice has the power of continuum while the depth is at leastℵ0. We have created a technique for proving that power-characteristicω-words are incomparable. We use this technique to show that this join-semilattice is not modular.