论文标题
公理化折纸平面
Axiomatizing Origami planes
论文作者
论文摘要
我们提供了基于折纸构造的Huzita-Justin Axioms的逻辑公理的基本几何形状的公理化变体。我们隔离了与自然类别的折纸构建体相对应的片段，例如毕达哥拉斯，欧几里得和完整的折纸结构。每个构造类别的折纸构造点的集合提供了相应的逻辑公理集的最小模型。 我们的公理化基于WU的正交几何形状的公理和Huzita-Justin Axioms的一些修改。如J.A. Makowsky（2018）。使用M. Ziegler（1982）的定理，这意味着不可确定的越越野字段的一阶理论是不可决定的，我们对折纸的公理化的一阶理论也是不可确定的。
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.
