Some properties of Boolean ordered sets. (English) Zbl 0904.06002

The author generalizes some results which are known about Boolean algebras, especially Boolean ordered sets. For example he proves that if \(S\) is a Boolean ordered set, then the Dedekind-MacNeille completion of \(S\) is a Boolean algebra. Further he gives a partial solution of the problem of the number of nonisomorphic finite Boolean sets having a given number of elements. Finally, he proves that every atomic Boolean set is generally distributive.


06A06 Partial orders, general
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[1] Halaš R.: Pseudocomplemented ordered sets. Arch. Math. (Brno) 29 (1993), 3-4, 153-160. · Zbl 0801.06007
[2] Halaš R.: Decompositions of directed set with zero. Math. Slovaca 45 (1995), no. 1, 9-17. · Zbl 0833.06001
[3] Chajda I., Rachůnek J.: Forbidden configurations of distributive and modular ordered sets. Order 5 (1989), 407-423. · Zbl 0674.06003
[4] Chajda I.: Complemented ordered sets. Arch. Math. (Brno) 28 (1992), 25-34. · Zbl 0785.06002
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