zbMATH — the first resource for mathematics

Note on orthocomplemented posets. II. (English) Zbl 0535.06003
[For Part I cf. Topology and measure III, Proc. Conf. Vitte/Hiddensee 1980, Part 1, 65-73 (1982; Zbl 0536.06002).]
The ortho-double of a poset P is the union of P and a second copy of P with reversed ordering (minimal and maximal elements of both are identified). There is shown that the ortho-double of P is isomorphic with the orthocomplemented poset of left and right intervals of P. The second proposition states that finite orthocomplemented posets have an even order and that every even number is an order of some orthocomplemented poset. The full classification of such posets of order \(\leq 10\) is also given.
Reviewer: J.Waszkiewicz

06A06 Partial orders, general
Zbl 0536.06002