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Partially ordered sets, and minimal systems of counterexamples

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Abstract

Given a finite setA with a partial ordering, in which certain order relations are known to hold, there is a least set of non-relations that must be established to conclude that no relations hold other than the known ones. This set of test cases can be cut down further if algebraic structure is involved. These observations generalize arguments used by Pigozzi and others in studying finite semigroups of operators on classes of algebras.

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Authors and Affiliations

  1. University of California, 94720-3840, Berkeley, CA, USA

    G. M. Bergman

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  1. G. M. Bergman
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Dedicated to Bjarni Jonsson on his 70th birthday

This work was done while the author was partly supported by NSF contracts MCS 82-02632 and DMS 85-02330.

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Bergman, G.M. Partially ordered sets, and minimal systems of counterexamples. Algebra Universalis 32, 13–30 (1994). https://doi.org/10.1007/BF01190814

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