## 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.

### MSC:

 06A06 Partial orders, general
Full Text:

### References:

 [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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