The Brooks-Jewett theorem for -triangular functions on difference posets and orthoalgebras

Abstract

We introduce k-triangular functions on difference posets and we prove a Brooks-Jewett-type theorem for such functions that are defined on a difference poset (or an effect algebra) satisfying the weak subsequential interpolation property. This result enables us to obtain the previously known Brooks-Jewett theorems for orthoalgebras and orthomodular lattices.