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On Set-Representable Orthocomplemented Difference Lattices

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Abstract

Matoušek introduced and axiomatized a notion of symmetric difference for orthocomplemented lattices (OMLs) called the orthocomplemented difference lattics (ODLs). We focus on the class of all ODLs that are set-representable and prove that this class is not locally finite by constructing an infinite three-generated set-representable ODL. This result answers a question posed by Matoušek and Pták. We also prove, by example, that not every concrete OML can be OML-embedded into an ODL.

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  1. Department of Mathematics, Physics, and Computer Science, Georgetown College, Georgetown, KY, USA

    Jianning Su

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  1. Jianning Su
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Correspondence to Jianning Su.

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Su, J. On Set-Representable Orthocomplemented Difference Lattices. Order 37, 621–636 (2020). https://doi.org/10.1007/s11083-020-09522-7

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  • DOI: https://doi.org/10.1007/s11083-020-09522-7

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