Zigzags of Finite, Bounded Posets and Monotone Near-Unanimity Functions and Jónsson Operations

Abstract

We define the notion of monotone operations admitted by partially ordered sets, specifically monotone near-unanimity functions and Jónsson operations. We then prove a result of McKenzie's in [8] which states that if a finite, bounded poset P admits a set of monotone Jónsson operations then it admits a set of monotone Jónsson operations for which the operations with even indices do not depend on their second variable. We next define zigzags of posets and prove various useful properties about them. Using these zigzags, we proceed carefully through Zadori's proof from [12] that a finite, bounded poset P admits a monotone near-unanimity function if and only if P admits monotone Jónsson operations.