Distributivity for Upper Continuous and Strongly Atomic Lattices

作者：Aazarz Marcin^*; Siemienczuk Krzysztof

来源：Studia Logica, 2017, 105(3): 471-478.

DOI：10.1007/s11225-016-9697-5

• Distributive lattice
• Strongly atomic lattice
• Upper continuous lattice
• Birk-hoff's conditions
• Covering conditions
• Locally distributive lattice
• Covering diamond

In the paper we introduce two conditions (D) and () 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 (). 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.

• 出版日期2017-6