Implication in sharply paraorthomodular and relatively paraorthomodular posets

Ivan Chajda, Davide Fazio, Helmut Länger, Antonio Ledda, Jan Paseka

Published 2023-01-23Version 1

In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie's theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.