Bachelor's degree
Until the 19th century, a bachelor's degree represented the first degree in a particular faculty, with Arts representing undergraduate study, thus the Bachelor of Civil Law (BCL) at Oxford and the Bachelor of Laws (LLB) at Cambridge, for example, were postgraduate degrees. Vestiges of this system still remain in the ancient universities, with Oxford and Cambridge awarding BAs for undergraduate degrees in both arts and sciences (although both award undergraduate BTh degrees through associated theological colleges, and Oxford awards BFA degrees in addition to the BA) and defining other bachelor's degrees (e.g. BPhil, BCL) as postgraduate awards equivalent to master's degrees, although many postgraduate bachelor's degrees have now been replaced by equivalent master's degrees (e.g. LLM for the LLB at Cambridge and MSc for the BSc at Oxford). The same historical usage of indicating an undergraduate degree by it being in the faculty of arts rather than being a bachelor's degree gives rise to the Oxbridge MA and the Scottish MA).
Propaedeutics
In the US, the equivalent of the propaedeutic diploma lies somewhere between an undergraduate certificate and an associate degree. Undergraduate certificates can be completed in as little as one semester (one-half of one academic year or about four months) and do not necessarily lead or contribute to any degree. Associate degrees (e.g. AA, AS) are typically earned after the first two years of the four- to five-year (in the US) course of study culminating in a baccalaureate degree; however, students matriculated in a bachelor's degree program are not usually awarded the associate degree en route (as is often the case when a doctoral student is awarded a master's degree en route). Additionally, there are first professional associate degrees (e.g. AAS, AGS) that do not necessarily lead or contribute to a bachelor's.