Labeled posets are universal

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. The homomorphicity order of k-posets is shown to be a distributive lattice. Homomorphicity orders of k-posets and k-lattices are shown to be universal in the sense that every countable poset can be embedded into them. Labeled posets are represented by directed graphs, and a categorical isomorphism between k-posets and their digraph representations is established.

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Erkko Lehtonen
• Keywords: Distributive Lattice, EJC 2007, EJC 2008, Homomorphicity Orders, Information Technology, Partially Ordered Sets