Abstract
We show that the 0–1 law fails in random orders of fixed dimension k, k≥3. In particular, we give an example of a first-order sentence ϕ, in the language of partial orders, which cannot have limiting probability 0 or 1 among random orders of dimension 3.
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Communicated by P. Hell
Research supported by ONR grant N00014-85-K-0769
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Winkler, P. A counterexample in the theory of random orders. Order 5, 363–368 (1989). https://doi.org/10.1007/BF00353655
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DOI: https://doi.org/10.1007/BF00353655