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Countable linear orders with disjoint infinite intervals are mutually orthogonal |
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| Authors: | Christian Delhommé Imed Zaguia |
| Affiliation: | 1. Laboratoire d’Informatique et de Mathématiques (LIM-ERMIT), Faculté des Sciences et Technologies, Université de la Réunion, PTU - 2, rue Joseph Wetzell, 97490 Sainte-Clotilde, France;2. Department of Mathematics and Computer Science, Royal Military College, P.O.Box 17000 Station Forces, Kingston, Ontario, K7K 7B4, Canada |
| Abstract: | Two linear orderings of a same set are perpendicular if the only self-mappings of this set that preserve them both are the identity and the constant mappings. Two linear orderings are orthogonal if they are isomorphic to two perpendicular linear orderings. We show that two countable linear orderings are orthogonal as soon as each one has two disjoint infinite intervals. From this and previously known results it follows in particular that each countably infinite linear ordering is orthogonal to itself. |
| Keywords: | Linearly ordered set Order preserving map Bichain Endomorphism Orthogonal orders Endomorphism-rigid relational structure |
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