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.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/4730 |
| Date | January 2009 |
| Creators | Martin, Eric |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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