@inbook{a1fab06df595497c947c99dfa29d15f6,
title = "Axiomatizing Origami Planes",
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{\textquoteright}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.",
keywords = "Axiom, Geometry, Interpretation, Origami, Undecidability",
author = "Lev Beklemishev and Anna Dmitrieva and Makowsky, {Johann A.}",
note = "Acknowledgements: The work of Lev Beklemishev and Anna Dmitrieva was supported by the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2019–2020 (grant No. 19-04-050) and by the Russian Academic Excellence Project “5–100”.",
year = "2024",
month = jul,
day = "26",
doi = "10.1007/978-3-031-47921-2_12",
language = "English",
isbn = "978-3-031-47920-5",
volume = "28",
series = "Outstanding Contributions to Logic",
publisher = "Springer",
pages = "353--377",
editor = "Nick Bezhanishvili and Rosalie Iemhoff and Fan Yang",
booktitle = "Dick de Jongh on Intuitionistic and Provability Logics",
address = "Germany",
edition = "1",
}