Axiomatizing Origami Planes

Lev Beklemishev, Anna Dmitrieva, Johann A. Makowsky

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract

We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita–Justin axioms for the origami constructions. We isolate the fragments corresponding to natural classes of origami constructions such as Pythagorean, Euclidean, and full origami constructions. The set of origami constructible points for each of the classes of constructions provides the minimal model of the corresponding set of logical axioms. Our axiomatizations are based on Wu’s axioms for orthogonal geometry and some modifications of Huzita–Justin axioms. We work out bi-interpretations between these logical theories and theories of fields as described in Makowsky (2018). Using a theorem of Ziegler (1982) which implies that the first order theory of Vieta fields is undecidable, we conclude that the first order theory of our axiomatization of origami is also undecidable.

Original languageEnglish
Title of host publicationDick de Jongh on Intuitionistic and Provability Logics
EditorsNick Bezhanishvili, Rosalie Iemhoff, Fan Yang
PublisherSpringer
Chapter12
Pages353-377
Number of pages25
Volume28
Edition1
ISBN (Electronic)978-3-031-47921-2
ISBN (Print)978-3-031-47920-5, 978-3-031-47923-6
DOIs
Publication statusPublished - 26 Jul 2024

Publication series

NameOutstanding Contributions to Logic
PublisherSpringer Cham
Volume28
ISSN (Print)2211-2758
ISSN (Electronic)2211-2766

Keywords

  • Axiom
  • Geometry
  • Interpretation
  • Origami
  • Undecidability

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