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arXiv 2204.07575math.LO
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奎斯塔-康威的名字是康托尔命令的延伸:一个关于超自然名字的法庭介绍

Les nombres de Cuesta-Conway comme extension des ordinaux de Cantor: une courte introduction aux nombres surréels

Labib Haddad

摘要:

On Cuesta-Conway numbers as an extension of Cantor's ordinals:A short introduction to surreal numbers.奎斯塔-康威数的类,超实数,可以简单地定义,从它们的标准形式(由序数索引的指数族)开始,作为实数和序数的扩展,从中很容易遵循加法,乘法和全序关系。这个类的一个构造产生一个实闭域的递增序列,可以说是初步的。给出了超实数类是全序交换实闭域这一著名结果的完整证明。

英文摘要:

On Cuesta-Conway numbers as an extension of Cantor's ordinals: A short introduction to surreal numbers. The class of Cuesta-Conway numbers, the surreal numbers, can be defined simply, starting from their normal forms (families of exponentials indexed by ordinals), as an extension of the reals and ordinals from which easily follow addition, multiplication, and total order relation. A construction of this class yields an increasing sequence of real-closed fields, preliminary, so to say. A complete proof is also given the well-known result that the class of surreal numbers is a totally ordered, commutative, real-closed field!

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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