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The undefinability of intersection from perpendicularity in the three-dimensional Euclidean geometry of lines

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Abstract

The undefinability in question is proved by constructing a bijection of lines preserving perpendicularity but not intersection.

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References

  1. Beth, Evert W.,The Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, 1965.

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  2. Lang, Serge,Algebra, Addison-Wesley, Reading, Mass, 1970.

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  3. Schwabhäuser, W. and Szczerba, L. W., ‘Relations on lines as primitive notions for Euclidean geometry’,Fundamenta Mathematicae 82 (1975), 347–355.

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Kramer, R. The undefinability of intersection from perpendicularity in the three-dimensional Euclidean geometry of lines. Geom Dedicata 46, 207–210 (1993). https://doi.org/10.1007/BF01264919

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  • DOI: https://doi.org/10.1007/BF01264919

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