论文标题
潜在无限的模型理论
A Model Theory for the Potential Infinite
论文作者
论文摘要
我们介绍了模型理论概念，该概念可以通过潜在的无限而不是实际的无限的概念来开发数学。潜在的无限被理解为一个动态概念，是无限延伸的有限。主要采用是对普遍量化器的解释，该量词具有隐性反思原理。每个通用量化都指无限期但有限的集合。量化集可能会增加，因此在通过量化参考后，进一步的参考通常使用较大的，仍然有限的集合。我们介绍了经典一阶逻辑的概念，并表明这些动态模型相对于通常的推理规则是合理的和完整的。此外，一组有限的公式需要增加模型的有限部分才能正确解释。
We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely extensible finite. The main adoption is the interpretation of the universal quantifier, which has an implicit reflection principle. Each universal quantification refers to an indefinitely large, but finite set. The quantified sets may increase, so after a reference by quantification, a further reference typically uses a larger, still finite set. We present the concepts for classical first-order logic and show that these dynamic models are sound and complete with respect to the usual inference rules. Moreover, a finite set of formulas requires a finite part of the increasing model for a correct interpretation.
