✍ Scribed by Reed Solomon
No coin nor oath required. For personal study only.
It is known that the spaces of orders on orderable computable ÿelds can represent all 0 1 classes up to Turing degree. We show that the spaces of orders on orderable computable abelian and nilpotent groups cannot represent 0 1 classes in even a weak manner. Next, we consider presentations of ordered abelian groups, and we show that there is a computable ordered abelian group for which no computable presentation admits a computable set of representatives for its Archimedean classes.
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In 1981, Chvatal defined the class of perfectly orderable graphs. This class of perfect graphs contains the comparability graphs and the triangulated graphs. In this paper, we introduce four classes of perfectly orderable graphs, including natural generalizations of the comparability and triangulate
A graph is called "perfectly orderable" if its vertices can be ordered in such a way that, for each induced subgraph F, a certain "greedy" coloring heuristic delivers an optimal coloring of F. No polynomial-time algorithm to recognize these graphs is known. We present four classes of perfectly order