| 21. | The verification that this structure is a distributive lattice with the required universal property is routine.
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| 22. | This provides an alternative definition of a Boolean algebra, namely as any complemented distributive lattice.
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| 23. | Let be a bounded distributive lattice, and let denote the topology on is generated by.
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| 24. | This condition is called "'distributivity "'and gives rise to distributive lattices.
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| 25. | The deduction theorem holds for all first-order theories with the usual non-distributive lattice.
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| 26. | However, in a ( bounded ) distributive lattice every element will have at most one complement.
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| 27. | Each pairwise Stone space is bi-homeomorphic to the bitopological dual of some bounded distributive lattice.
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| 28. | However, it is still possible that two such terms denote the same element of the distributive lattice.
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| 29. | In the case of distributive lattices such an " M " is always a prime ideal.
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| 30. | These are laws of Boolean algebra whence the underlying poset of a Boolean algebra forms a distributive lattice.
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