Subset Based Properties of Partially Ordered Sets

Abstract The theory of partially ordered sets (posets, for short) proved to have crucial applications in at least two major fields of computer science: concurrency theory and the semantics of programming languages. In these fields, properties like discreteness, observability, generability, and completeness play an important role. The first three of them have been studied in the literature only for the particular case of finite cardinals and/or at most countable posets. In this paper we generalize the properties of discreteness, observability, and generability by allowing arbitrarily large cardinals. The results we obtain extend in a proper way many of the results obtained until now regarding these properties [4, 5]. Concerning completeness properties, we adopt a general definition using subset systems, and then investigate the relationships between various concepts of completeness