Journal ArticleDOI
Anordnungsräume unter der Moulton Konstruktion und Ebenen der Lenz Klasse III
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In this paper, it was shown that there exist projective planes of Lenz-Class III which are not isomorphic to any generalized Moulton plane, and a wide variety of non-Moulton planes of Class III.1 and III.2.Abstract:
As we have shown in [27] there do exist projective planes of Lenz-Class III which are not isomorphic to any (generalized) Moulton plane. We will go into some detail concerning the construction of these planes, present a wide variety of non-Moulton planes of Class III.1 and III.2, and determine their spaces of orderings. In particular, for any two-power z, we construct a Cartesian group C which satisfies Yaqub's criterion and whose distrubutor has index z in the multiplicative loop of C.read more
Citations
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The axiomatics of ordered geometry: I. Ordered incidence spaces
TL;DR: The authors present a survey of the theory of betweenness and separation from its beginning with Pasch's 1882 Vorlesungen uber neuere Geometrie to the present.
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Formal power series over Cartesian groups and their spaces of orderings
TL;DR: In this paper, the authors introduce formal power series over Cartesian groups on arbitrary, ordered loops, and show that, under a weak additional hypothesis, their spaces of orderings are as in the classical case.
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On multiple-valued ordered projective planes
TL;DR: In this article, the notion of compatibility between multiple-valued orderings and epimorphisms of projective planes has been studied and its algebraic counterpart has been investigated using the machinery of lifting orderings via places.
References
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Book
Orderings, valuations, and quadratic forms
TL;DR: The reduced theory of quadratic forms Compatibility between valuations and orderings Compatibility between values and preorderings Appendix: Henselian Fields and 2-Henselian fields $T$-forms under a compatible valuation Introduction to fans Appendix: Superpythagorean fields The representation problem: solution for fans as mentioned in this paper.
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A simple non-Desarguesian plane geometry
TL;DR: The necessary and sufficient condition that a plane geometry fulfilling the plane axioms 1 1-2, II, III may be a part of (or set in) a spatial geometry of more than two dimensions fulfllling DESARGUES's theorem is given in this paper.