The algebraic study of formal languages shows thatω-rational languages are exactly the sets recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first define a red...

We generalize results concerning C0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local C0-semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norm...

We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when non-empty subset is base. Moreover, we give characterization base to be subsemigroup show that have same cardinality. Finally, complement union all maximal proper left ideal.