Posets for Con gurations

We de ne families of posets ordered by pre xes as the coun terpart of the usual families of con gurations ordered by subsets On these objects we de ne two types of morphism event and order morphisms re sulting in categories FPos and FPos We then show the following Families of posets in contrast to families of con gurations are always prime algebraic in fact the category FPos is equivalent to the category of prime algebraic domains On the level of events FPos is equivalent to the category of prime alge braic domains with an additional relation encoding event identity The abstract event identity relation can be used to characterize con crete relations between events such as binary con ict and causal ow One can characterize a wide range of event based models existing in the literature as families of posets satisfying certain speci c structural conditions formulated in terms of event identity In CONCUR W R Cleaveland Ed Lecture Notes in Computer Science Springer Verlag pp