A note on congruences of semilattices with sectionally finite height |
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| Authors: | Josep Maria Font Tommaso Moraschini |
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| Affiliation: | 1. Department of Probability, Logic, and Statistics, University of Barcelona, E-08071, Barcelona, Spain
2. Department of Logic, History and Philosophy of Science, University of Barcelona, E-08071, Barcelona, Spain
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| Abstract: | We present a bijective correspondence between congruences of semilattices with sectionally finite height (i.e., meet-semilattices whose principal downsets have finite length) and certain special subsets of their universes. We characterize these subsets from a purely order-theoretic point of view and prove that the bijection coincides with the Leibniz operator of abstract algebraic logic. |
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