Axiomatizing Origami planes

Anna Dmitrieva, Lev Beklemishev, Johann Makowsky

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


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 sets 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 J.A. Makowsky (2018). Using a theorem of M. 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 Nature
ISBN (Electronic)978-3-031-47921-2
ISBN (Print)978-3-031-47920-5, 978-3-031-47923-6
Publication statusAccepted/In press - 2024

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