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Beklemishev, Lev, Dmitrieva, Anna 
ORCID: https://orcid.org/0000-0001-7551-6122 and Makowsky, Johann A.
(2024)
Axiomatizing Origami Planes.
In:
Dick de Jongh on Intuitionistic and Provability Logics.
Outstanding Contributions to Logic, 28
(1).
Springer, pp. 353-377.
ISBN 978-3-031-47920-5
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.
| Item Type: | Book Section |
|---|---|
| Additional Information: | 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”. |
| Uncontrolled Keywords: | axiom,geometry,interpretation,origami,undecidability,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609 |
| Faculty \ School: | Faculty of Science Faculty of Science > School of Mathematics (former - to 2024) |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 31 May 2024 10:30 |
| Last Modified: | 30 Sep 2024 13:30 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/95352 |
| DOI: | 10.1007/978-3-031-47921-2_12 |
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