Nonclassical properties of a discrete geometries space (Q844351)

The author continues his study of the ``discrete geometric spaces'' he has introduced earlier in [Cybern. Syst. Anal. 42, No. 5, 631--640 (2006; Zbl 1117.68074)]. These are defined in algebraic terms, by giving some geometric interpretation to certain formulas associated to sets of real numbers that depend on a certain parameter. It seems that the main result in this paper is Theorem 5, which states that a certain model of ``discrete Euclidean geometry (DEG)'' does not satisfy an unstated ``Euclidean axiom of ordering'', which is not that surprising, given that it is not clear what axioms DEG satisfies at all. The language used, such as the above axiom name, and the fact that the only paper cited that was not written by the author is Riemann's \textit{Über die Hypothesen welche der Geometrie zu Grunde liegen}, makes it hard to judge what the aim of this undertaking is or whether it was achieved.