Algebraic quantization of causal sets

A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebr aization and quantum interpretation of finitary topological spaces due to Z apatrin and this author. To be able to apply the latter procedure to causal sets Sorkin's 'semantic switch' from 'partially ordered sets as finitary t opological spaces' to 'partially ordered sets as locally finite causal sets ' is employed. The result is the definition of 'quantum causal sets'. Such a procedure and its resulting definition are physically justified by a prop erty of quantum causal sets that meets Finkelstein's requirement for 'quant um causality' to be an immediate, as well as an algebraically represented, relation between events for discrete locality's sake. The quantum causal se ts introduced here are shown to have this property by direct use of a resul t from the algebraization of finitary topological spaces due to Breslav, Pa rfionov, and Zapatrin.