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Positive definitions of segment congruence in terms of segment inequality

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Summary.

It is shown that segment congruence can be defined by means of a positive existential definition in terms of segment inequality in several geometries over Archimedean ordered fields, and that it can be defined by means of a positive sentence in n-dimensional Euclidean geometry over arbitrary ordered fields.

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Authors and Affiliations

  1. Department of Integrative Studies, Arizona State University – West Campus, P. O. Box 37100, Phoenix, AZ, 85069-7100, USA

    Victor Pambuccian

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  1. Victor Pambuccian
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Correspondence to Victor Pambuccian.

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Manuscript received: March 2, 2005 and, in final form, October 3, 2005.

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Pambuccian, V. Positive definitions of segment congruence in terms of segment inequality. Aequ. math. 72, 243–253 (2006). https://doi.org/10.1007/s00010-006-2844-8

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  • DOI: https://doi.org/10.1007/s00010-006-2844-8

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