论文标题
半真实线的半构建方法
A Semi-Constructive Approach to the Hyperreal Line
论文作者
论文摘要
使用最新的tarskian语义的替代方案，用于一阶逻辑，称为$ \ textit {可能的语义} $，我引入了一种替代方法，用于非标准分析，该方法仍然在\ textit {semi-structive}数学学的范围内，即，不超过选择的Axiom expection axiom expectect ofectent overent overent overent of Axiom的axiom axiom的范围。我将$ f \ it { - hyperreal} $ $ \ it {line} $ {^\ dagger \！\ mathcal {r}} $作为一种可能性结构，并表明它具有经典超大型线的许多基本属性，例如转移原理和饱和原则。我讨论了$ {^\ Dagger \！\ Mathcal {r}} $的技术优势，而不是其他一些非标准分析的替代方法，并认为它非常适合解决某些哲学和方法论问题，这些问题已针对非标准方法对普通数学的应用而提出。
Using a recent alternative to Tarskian semantics for first-order logic, known as $\textit{possibility semantics}$, I introduce an alternative approach to nonstandard analysis that remains within the bounds of \textit{semi-constructive} mathematics, i.e., does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. I define the $F\it{-hyperreal}$ $\it{line}$ ${^\dagger\!\mathcal{R}}$ as a possibility structure and show that it shares many fundamental properties of the classical hyperreal line, such as a Transfer Principle and a Saturation Principle. I discuss the technical advantages of ${^\dagger\!\mathcal{R}}$ over some other alternative approaches to nonstandard analysis and argue that it is well-suited to address some of the philosophical and methodological concerns that have been raised against the application of nonstandard methods to ordinary mathematics.
