Klein-Beltrami模型。第四部分

IF 1 Q1 MATHEMATICS

Formalized Mathematics Pub Date : 2020-04-01 DOI:10.2478/forma-2020-0002

Roland Coghetto

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引用次数: 0

摘要

Timothy Makarios (with Isabelle/HOL1)和John Harrison (with HOL-Light2)证明了“双曲平面的Klein-Beltrami模型满足Tarski的所有公理，除了他的欧几里得公理”[2]，[3]，[4,5]。对于Mizar系统[1]，我们使用了Tim Makarios的硕士论文[10]中的一些思想来形式化验证平行公设独立性所需的一些定义和引理。在本文中，作为[8]的延续，我们证明了我们构造的模型满足[11]和相关Mizar文章中形式化的分段构造公理、中间恒等式公理和Pasch due to Tarski公理。

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Klein-Beltrami model. Part IV

Summary Timothy Makarios (with Isabelle/HOL1) and John Harrison (with HOL-Light2) shown that “the Klein-Beltrami model of the hyperbolic plane satisfy all of Tarski’s axioms except his Euclidean axiom” [2],[3],[4, 5]. With the Mizar system [1] we use some ideas taken from Tim Makarios’s MSc thesis [10] to formalize some definitions and lemmas necessary for the verification of the independence of the parallel postulate. In this article, which is the continuation of [8], we prove that our constructed model satisfies the axioms of segment construction, the axiom of betweenness identity, and the axiom of Pasch due to Tarski, as formalized in [11] and related Mizar articles.

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来源期刊

Formalized Mathematics MATHEMATICS-

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.