A remark to orthomodular lattices with almost orthogonal set of atoms. (English) Zbl 0762.06002
Measure theory, Proc. 2nd Winter Sch., Liptovský Ján/Czech. 1990, 175-176 (1990).
[For the entire collection see Zbl 0725.00004.]
The authors study atomic orthomodular lattices (OMLs) with the following property: For each atom \(e_{0}\) there is an integer \(n(e_{0})\) such that each \(k\)-tuple of atoms \(e_{1}, \ldots, e_{k}\) with \(e_{i-1} \not\leq e_{i}^{\perp}\) (\(i=1, \ldots, k\)) satisfies \(\text{card}\{e_{0}, \ldots, e_{k}\} \leq n(e_{0})\). It is proved that these OMLs allow embeddings into products of finite OMLs.
The authors study atomic orthomodular lattices (OMLs) with the following property: For each atom \(e_{0}\) there is an integer \(n(e_{0})\) such that each \(k\)-tuple of atoms \(e_{1}, \ldots, e_{k}\) with \(e_{i-1} \not\leq e_{i}^{\perp}\) (\(i=1, \ldots, k\)) satisfies \(\text{card}\{e_{0}, \ldots, e_{k}\} \leq n(e_{0})\). It is proved that these OMLs allow embeddings into products of finite OMLs.
Reviewer: M.Navara (Praha)
