皮亚诺算术,游戏和下降递归

IF 0.6 2区 数学 Q2 LOGIC
Emanuele Frittaion
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引用次数: 0

摘要

我们通过初等下降递归[8]的视角分析Coquand对Peano算术[6]的博弈论解释。在Coquand的博弈语义中,获胜策略对应于无限无切证明,切消除对应于这些获胜策略之间的争论。切消的证明,即这种辩论最终终止的证明,是通过对某些序数相互作用序列的超限归纳法得到的。在本文中,我们提供了Coquand证明的一个直接实现,它允许我们通过下降递归函数来描述获胜策略。作为一个副产品,我们得到了另一个关于可证明递归函数和泛函的著名结果的证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Peano arithmetic, games and descent recursion
We analyze Coquand's game-theoretic interpretation of Peano Arithmetic [6] through the lens of elementary descent recursion [8]. In Coquand's game semantics, winning strategies correspond to infinitary cut-free proofs and cut elimination corresponds to debates between these winning strategies. The proof of cut elimination, i.e., the proof that such debates eventually terminate, is by transfinite induction on certain interaction sequences of ordinals. In this paper, we provide a direct implementation of Coquand's proof, one that allows us to describe winning strategies by descent recursive functions. As a byproduct, we obtain yet another proof of well-known results about provably recursive functions and functionals.
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来源期刊
CiteScore
1.40
自引率
12.50%
发文量
78
审稿时长
200 days
期刊介绍: The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.
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