• Corpus ID: 119145928

Affine planes, ternary rings, and examples of non-Desarguesian planes

@article{Ivanov2016AffinePT,
  title={Affine planes, ternary rings, and examples of non-Desarguesian planes},
  author={Nikolai V. Ivanov},
  journal={arXiv: Combinatorics},
  year={2016}
}
  • N. V. Ivanov
  • Published 18 April 2016
  • Mathematics
  • arXiv: Combinatorics
The paper is devoted to a detailed self-contained exposition of a part of the theory of affine planes leading to a construction of affine (or, equivalently, projective) planes not satisfying the Desarques axiom. It is intended to complement the introductory expositions of the theory of affine and projective planes. A novelty of our exposition is a new notation for the ternary operation in a ternary ring, much more suggestive than the standard one. 
3 Citations
The de Bruijn-Erd\"os-Hanani theorem
The present paper is devoted to a somewhat idiosyncratic account of the theorem of de Bruijn–Erdös and Hanani from the combinatorics of finite geometries and its various proofs. Among the proofs
Can one design a geometry engine? On the (un)decidability of affine Euclidean geometries
TLDR
It is shown here using elementary model theoretic tools that the universal first order consequences of any geometric theory of Pappian planes which is consistent with the analytic geometry of the reals is decidable.
Can one design a geometry engine?
  • J. Makowsky
  • Mathematics
    Annals of Mathematics and Artificial Intelligence
  • 2018
TLDR
It is shown here using elementary model theoretic tools that the universal first order consequences of any geometric theory T of Pappian planes which is consistent with the analytic geometry of the reals is decidable.

References

SHOWING 1-8 OF 8 REFERENCES
Projective planes I
Foundations of projective geometry
That's it, a book to wait for in this month. Even you have wanted for long time for releasing this book foundations of projective geometry; you may not be able to get in some stress. Should you go
1999; 1st edition: Macmillam
  • New York,
  • 1959
Hoboken
  • NJ,
  • 1986
Survey of non-Desarguesian planes, Notices of the AMS, V
  • 2007