Zuzana Haniková
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引用次数: 1

摘要

Vop\v{e}nka的可选集理论既可以被视为一种进化,也可以被视为一种革命:它是基于他以前对非标准宇宙的经验,受到Skolem对非标准算术模型的构建的启发,并且它的开始被明确地提到是为了将罗宾逊的非标准分析公式化。Vop\v{e}nka更喜欢在公理化理论中工作,而不是研究它的各个模型;他还通过这个棱镜观察了非经典数学的其他领域。本文是对可选集合论的数学邻域映射的贡献,同时,它提出了一个挑战,即更详细地分析最终影响可选集合论的哲学联系的起源和结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století
Vop\v{e}nka's Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem's construction of a nonstandard model of arithmetic, and its inception has been explicitly mentioned as an attempt to axiomatize Robinson's Nonstandard Analysis. Vop\v{e}nka preferred working in an axiomatic theory to investigating its individual models; he also viewed other areas of nonclassical mathematics through this prism. This article is a contribution to the mapping of the mathematical neighbourhood of the Alternative Set Theory, and at the same time, it submits a challenge to analyze in more detail the genesis and structure of the philosophical links that eventually influenced the Alternative Set Theory.
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