翻译中发现：Hudetz 纲领的极限
Found in Translation: at the limits of the Hudetz program
AI总结：
本文分析了一对广义理论在可相互定义意义上的等价性，针对非一阶逻辑表述的理论，推广了基于翻译的相对可解释性理论，提出在数学语言中而非相对特定结构的可定义性说明。
摘要：
本文旨在分析当我们说一对广义理解的理论在可相互定义的意义上等价时，这意味着什么。对于用一阶逻辑表述的理论，我们已有一种自然且被充分理解的机制来处理此问题：基于翻译的相对可解释性理论。然而，科学与数学（特别是物理学）中的许多重要理论虽被精确表述，却并非自然地用一阶逻辑或任何明显的语言来阐述。在本文中，我们计划推广普通的解释理论以容纳此类理论，提供一种说明，其中可定义性并非指相对于特定结构的可定义性，而是没有此类保留的可定义性：在数学语言中可定义。
英文摘要：
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we already have a natural and well-understood device for addressing this problem: the theory of relative interpretability as based on translation. However, many important theories in the sciences and mathematics (and, in particular, physics) are precisely formulated but are not naturally articulated in first order logic or any obvious language at all. In this paper, we plan to generalize the ordinary theory of interpretation to accommodate such theories by offering an account where definability does not mean definability relative to a particular structure, but rather definability without such reservations: definable in the language of mathematics.
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。
