Betweenness of partial orders
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We construct a monadic second-order sentence that characterizes the ternary relations that are the betweenness relations of finite or infinite partial orders. We prove that no first-order sentence can do that. We characterize the partial orders that can be reconstructed from their betweenness relations. We propose a polynomial time algorithm that tests if a finite relation is the betweenness of a partial order.
2006 ◽
Vol 41
(7)
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pp. 739-762
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2014 ◽
Vol 61
(1)
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pp. 51-78
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