Monotone Jónsson operations and near unanimity functions (Q1842598)

The concepts of nonextendible colored posets and zigzags of a poset are introduced. Some important properties of zigzags are proven. By using them, the author gives a proof of the well-known conjecture that any finite bounded poset which admits Jónsson operations, also admits a near-unanimity function. An infinite poset is presented showing that finiteness cannot be dropped in this conjecture.