The Simplest Axiom System for Plane Hyperbolic Geometry Revisited

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Using the axiom system provided by Carsten Augat in [1], it is shown that the only 6-variable statement among the axioms of the axiom system for plane hyperbolic geometry (in Tarski's language LB≡), we had provided in [3], is superfluous. The resulting axiom system is the simplest possible one, in the sense that each axiom is a statement in prenex form about at most 5 points, and there is no axiom system consisting entirely of at most 4-variable statements.

Original languageEnglish (US)
Pages (from-to)347-349
Number of pages3
JournalStudia Logica
Volume97
Issue number3
DOIs
StatePublished - Apr 1 2011

Keywords

  • Euclidean geometry
  • Hyperbolic geometry
  • axiom system
  • betweenness and equidistance
  • simplicity

ASJC Scopus subject areas

  • Logic
  • History and Philosophy of Science

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