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The Simplest Axiom System for Hyperbolic Geometry Revisited, Again

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Abstract

Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield two simpler axiom systems for absolute geometry.

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References

  1. Alama, J., Tipi: A TPTP-based theory development environment emphasizing proof analysis, arXiv preprint arXiv:1204.0901, 2012.

  2. Augat, C., Ein Axiomsystem für die hyperbolischen Ebenen über euklidischen Körpern, Ph.D. thesis, University of Stuttgart, 2008.

  3. Pambuccian, V., Simplicity, Notre Dame Journal of Formal Logic 29(3):396–411, 1988.

  4. Pambuccian V.: Simplicity. Notre Dame Journal of Formal Logic 29(3), 396–411 (1988)

    Article  Google Scholar 

  5. Pambuccian, V., The simplest axiom system for plane hyperbolic geometry revisited, Studia Logica 97(3):347–349, 2011.

    Google Scholar 

  6. Rigby J. F. Axioms for absolute geometry, Canadian Journal of Mathematics 20:158–181, 1968.

    Google Scholar 

  7. Rigby, J. F., Congruence axioms for absolute geometry, Mathematical Chronicle 4:13–44, 1975.

    Google Scholar 

  8. Scott, D., Dimension in elementary euclidean geometry, Studies in Logic and the Foundations of Mathematics 27:53–67, 1959.

    Google Scholar 

  9. Tarski, A., What is elementary geometry, in L. Henkin, P. Suppes, and A. Tarski (eds.), The Axiomatic Method, with Special Reference to Geometry ad Physics, North-Holland, Amsterdam, 1959, pp. 16–29.

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Correspondence to Jesse Alama.

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Alama, J. The Simplest Axiom System for Hyperbolic Geometry Revisited, Again. Stud Logica 102, 609–615 (2014). https://doi.org/10.1007/s11225-013-9509-0

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