Modularity in the Semilattice of ω-Words
Jānis Buļs, Edmunds Cers · Journal of Discrete Mathematics · 2014
A partial ordering of ω-words can be introduced with regard to whether an ω-word can be transformed into another by a Mealy machine. It is known that the poset of ω-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 least ℵ0 . We have created a technique for proving that power-characteristic ω-words are incomparable. We use this technique to show that this join-semilattice is not modular.