论文标题
建设性的Ackermann的解释
Constructive Ackermann's interpretation
论文作者
论文摘要
本文的主要目的是制定Ackermann关于有限集理论和算术的建设性类似物。我们将看到，Heyting Arithmetic与$ \ Mathsf {Czf^{fin}} $，$ \ Mathsf {czf} $ bi-Mathsf {czf^{fin}} $。我们还基于Fleischmann的公式层次结构的修改以及一组$ \ m varsf {czf} $的模型，我们还基于fleischmann的层次结构的修改以及$ \ \米的模型a {c，我们还研究了$ \ mathsf} $ \ math的模型{c， finality $ \ mathsf {izf} $。
The main goal of this paper is to formulate a constructive analogue of Ackermann's observation about finite set theory and arithmetic. We will see that Heyting arithmetic is bi-interpretable with $\mathsf{CZF^{fin}}$, the finitary version of $\mathsf{CZF}$. We also examine bi-interpretability between subtheories of finitary $\mathsf{CZF}$ and Heyting arithmetic based on the modification of Fleischmann's hierarchy of formulas, and the set of hereditarily finite sets over $\mathsf{CZF}$, which turns out to be a model of $\mathsf{CZF^{fin}}$ but not a model of finitary $\mathsf{IZF}$.
