We will focus on shift spaces over infinite alphabets via C*-algebra theory. In particular, we propose that the shift space should be the boundary path space of an ultragraph (ultragraphs generalize directed graphs and their associated C*-algebras model both Exel-Laca and graph C*-algebras).

After introducing ultragraphs we show that, for a large class of ultragraphs, the associated edge shift space (boundary path space) has a nice topological description. Furthermore, via partial crossed product construction, we give an idea how to show that if two (possibly infinite) ultragraphs have edge shifts that are conjugate, via a conjugacy that preserves length, then the associated ultragraph C*-algebras are isomorphic.