We show that the 2-crown is not coproductive, which is to say that the class of those bounded distributive lattices whose Priestley spaces lack any copy of the 2-crown is not productive. We do this by first exhibiting a general construction to handle questions of this sort. We then use a particular instance of this constrution, along with some of the combinatorial features of projective planes, to show that the 2-crown is not coproductive.
2000 Mathematics Subject Classification.Primary 06D55, 06A11, 54F05 Secondary 06D20, 03C05
Key words and phrases.distributive lattice Priestley duality poset first-order definable
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