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Seminars "Proof Theory" and "Logic Online Seminar"
November 2, 2020 18:30, Moscow, Steklov Mathematical Institute (8 Gubkina), room 313 + Zoom
 


Axiomatizing Origami planes

Anna Dmitrieva

Institute for Logic, Language and Computation, University of Amsterdam
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MP4 250.9 Mb

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Anna Dmitrieva



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 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.
Joint work with L. Beklemishev and J.A. Makowsky.

Language: English
 
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