Sergiu Rudeanu
Boolean-Based Ordered Monoids

Abstract.
Boolean-based mathematics is the attempt to establish analogues of several mathematical notions and theorems when their universe of discourse is replaced by a Boolean algebra. In this note we survey some elements of Boolean-based algebra and tackle the study of Boolean-based ordered algebraic structures. We determine all Boolean-based ordered and lattice-ordered groupoids and monoids, whereas Boolean-based ordered groups do not exist. We also show that a result obtained in [8] yields a new proof of a theorem due to Wiener [9].