From absolute to affine geometry in terms of point-reflections, midpoints, and collinearity

Jesse Alama, Victor Pambuccian

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We investigate equational theories expressed in terms of the point-reflection operation δ and the midpoint operation μ that lie strictly between the absolute and the affine theory, proving a number of dependencies and independencies in the process. Several universal theories enlarged with the collinearity predicate also lie strictly between the absolute and the affine theory. The independence models and several proofs were obtained by Tipi, an aggregate of automatic theorem provers. To show that no set of equations with at most three variables can axiomatize the affine theory is left as an open problem.

Original languageEnglish (US)
Pages (from-to)11-24
Number of pages14
JournalNote di Matematica
Volume36
Issue number1
DOIs
StatePublished - 2016

Keywords

  • Affine geometry
  • Automatic theorem proving
  • Axioms
  • Collinearity
  • Independence
  • Midpoints
  • Point-reflections

ASJC Scopus subject areas

  • Mathematics(all)

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