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On completion of cyclically ordered sets. (English) Zbl 0636.06004
A cyclic order on a set G is a ternary relation C on G, which is: (i) asymmetric, i.e. (x,y,z)$$\in C$$ implies (z,y,x)$${\bar \in}C$$, (ii) cyclic, i.e. (x,y,z)$$\in C$$ implies (y,z,x)$$\in C$$, and (iii) transitive, i.e. (x,y,z)$$\in C$$ and (x,z,u)$$\in C$$ together imply (x,y,u)$$\in C.$$
If, moreover, card $$G\geq 3$$, and for any three pairwise different elements either (x,y,z)$$\in C$$ or (z,y,x)$$\in C$$ then C is linear, and (G,C) is called a linearly cyclically ordered set or a cycle. Earlier [Czech. Math. J. 34(109), 322-333 (1984; Zbl 0551.06002)] the first author has constructed a completion of cycles by means of cuts. In this note the authors give another construction of a completion, which can be applied to a larger class of monodimensional cyclically ordered sets.
Reviewer: S.Gacsályi

##### MSC:
 06A06 Partial orders, general 06B23 Complete lattices, completions
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##### References:
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