Abstract. Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. Obtaining such axiomatizations in concurrency theory often turns out to be difficult, even in the setting of simple languages like BCCSP. This has raised a host of open questions that have been the subject of intensive research in recent years. Most of these questions have been settled over BCCSP, either positively by giving a finite complete axiomatization, or negatively by proving that such an axiomatization does not exist. Still some open questions remain. This paper reports on these results, and on the state-of-the-art in axiomatizations for richer process algebras with constructs like sequential and parallel composition. 1

Abstract. We present a new technique for studying the w-axiomatizability of the semantics in the ltbt-spectrum. Although Fokkink et al. have recently solved most of the problems still open, our main goal is to shed light on them, and to simply and unify their proofs. Besides, we will focus on preorders (and make a fundamental use of the axiom for ready simulation semantics) instead of equivalences, since they give rise to much simpler proofs. 1