Partializing Stone Spaces using SFP domains

In this paper we investigate the problem of \partializing" Stone spaces by \Sequence of Finite Posets" (SFP) domains. More speciically, we introduce a suitable subcategory SFP m of SFP which is naturally related to the special category of Stone spaces 2-Stone by the functor MAX, which associates to each object of SFP m the space of its maximal elements. The category SFP m is closed under limits as well as many domain construc-tors, such as lifting, sum, product and Plotkin powerdomain. The functor MAX preserves limits and commutes with these constructors. Thus, SFP domains which \partialize" solutions of a vast class of domain equations in 2-Stone, can be obtained by solving the corresponding equations in SFP m. Furthermore, we compare two classical partializations of the space of Milner's Synchronization Trees using SFP domains (see 3], 15]). Using the notion of \rigid" embedding projection pair, we show that the two domains are not isomorphic, thus providing a negative answer to an open problem raised in 15].