Jumping automata are finite that read their input in a non-consecutive manner, disregarding the order of letters word. We introduce and study jumping over infinite words. Unlike setting words, which has been well studied, for words it is not clear how can be reordered. To this end, we consider three semantics: word some so no letter overlooked, permute windows given size k, an existentially-qua...

We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper n-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph G satisfies the connected existentially closed property and admits a homomorphism to H, then it admits continuum-many distinguishing homomorphism...

Along the lines of classical categorical type theory for total functions, we establish correspondence results between certain classes of partial equational theories on the one hand and suitable classes of categories having certain finite limits on the other hand. E.g., we show that finitary partial theories with existentially conditioned equations are essentially the same as cartesian categorie...