Abstract
In the paper we introduce two conditions (D) and (\(\hbox {D}^*\)) which are strengthenings of Birkhoff’s conditions. We prove that an upper continuous and strongly atomic lattice is distributive if and only if it satisfies (D) and (\(\hbox {D}^*\)). This result extends a theorem of R.P. Dilworth characterizing distributivity in terms of local distributivity and a theorem of M. Ward characterizing distributivity by means of covering diamonds.
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Presented by Andrzej Indrzejczak
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Łazarz, M., Siemieńczuk, K. Distributivity for Upper Continuous and Strongly Atomic Lattices. Stud Logica 105, 471–478 (2017). https://doi.org/10.1007/s11225-016-9697-5
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DOI: https://doi.org/10.1007/s11225-016-9697-5