Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Axiomatizing Origami planes   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.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int