| 11. | Each Priestley space is isomorphic to the Priestley dual of some bounded distributive lattice.
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| 12. | Heyting algebras are an example of distributive lattices where some members might be lacking complements.
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| 13. | This distributivity law defines the class of "'distributive lattices " '.
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| 14. | Such structures are called completely distributive lattices.
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| 15. | See the article on completely distributive lattices.
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| 16. | In distributive lattices, complements are unique.
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| 17. | Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.
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| 18. | A distributive lattice is complemented if and only if it is bounded and relatively complemented.
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| 19. | In fact this is the traditional axiomatization of Boolean algebra as a complemented distributive lattice.
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| 20. | The result is a distributive lattice and is used in Birkhoff's representation theorem.
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