Using coloured ordered sets to study finite-level full dualities

作者：Davey Brian A^*; Haviar Miroslav; Pitkethly Jane G

来源：Algebra Universalis, 2010, 64(1-2): 69-100.

DOI：10.1007/s00012-010-0090-3

• Natural duality
• full duality
• Priestley duality

We consider all the full dualities for the class of finite bounded distributive lattices that are based on the three-element chain 3. Under a natural quasi-order, these full dualities form a doubly algebraic lattice F(3). Using Priestley duality. we establish a correspondence between the elements of F(3) adn special enriched ordered sets, which we call 'coloured ordered sets'. We can then use combinatorial arguments to show that teh lattice F(a) has cardinality 2(0)(chi) and is non-modular. This is the first investigation into the structure of an infinite lattice of finite-level full dualities.

• 出版日期2010-10