Halaš, Radomír Some properties of Boolean ordered sets. (English) Zbl 0904.06002 Czech. Math. J. 46, No. 1, 93-98 (1996). 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. Reviewer: R.Majovská (Horni-Sucha) Cited in 7 Documents MSC: 06A06 Partial orders, general Keywords:Boolean ordered sets; Dedekind-MacNeille completion; nonisomorphic finite Boolean sets; atomic Boolean set PDF BibTeX XML Cite \textit{R. Halaš}, Czech. Math. J. 46, No. 1, 93--98 (1996; Zbl 0904.06002) Full Text: EuDML OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.