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 language | English (US) |
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Pages (from-to) | 347-349 |
Number of pages | 3 |
Journal | Studia Logica |
Volume | 97 |
Issue number | 3 |
DOIs | |
State | Published - Apr 1 2011 |
Keywords
- Euclidean geometry
- Hyperbolic geometry
- axiom system
- betweenness and equidistance
- simplicity
ASJC Scopus subject areas
- Logic
- History and Philosophy of Science