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Implicative posets. (English) Zbl 0813.06001
Summary: Implicative posets are defined and some properties of implicative posets are studied. Mainly it is proved that (1) every implicative poset is distributive, and (2) the Mac-Neille completion of an implicative poset is implicative.
There already exists a well-developed theory of implicative lattices and semilattices due to Curry (1963), Monteiro (1955), Nemitz (1965), Smith (1972) and Stone (1977). In this paper it is shown that a large part of this theory may be extended to implicative posets without making use of the meet operation or even assuming that it exists.

MSC:
06A06 Partial orders, general
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