几何逻辑中的Glivenko序类与构造切消

IF 0.3 4区 数学 Q1 Arts and Humanities
Giulio Fellin, Sara Negri, Eugenio Orlandelli
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引用次数: 2

摘要

第二作者在早期的工作中给出了经典的、直觉的和最小无穷逻辑的具有几何规则的序列演算的切消证明的构造。这是通过一个过程来实现的,其中非建设性的超限归纳在序数的可交换和被两个实例的布劳维尔的条形归纳法取代。在推导可嵌入性概念的基础上,引入一种新的建立良好的关系,使得结构规则的可容许性证明不需要序性。此外,对于七个(有限的)Glivenko序列类,经典逻辑对直觉逻辑/最小逻辑的保守性也适用于相应的无限类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Glivenko sequent classes and constructive cut elimination in geometric logics

Glivenko sequent classes and constructive cut elimination in geometric logics

A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric rules—given in earlier work by the second author—is presented. This is achieved through a procedure where the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. The proof of admissibility of the structural rules is made ordinal-free by introducing a new well-founded relation based on a notion of embeddability of derivations. Additionally, conservativity for classical over intuitionistic/minimal logic for the seven (finitary) Glivenko sequent classes is here shown to hold also for the corresponding infinitary classes.

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来源期刊
Archive for Mathematical Logic
Archive for Mathematical Logic MATHEMATICS-LOGIC
CiteScore
0.80
自引率
0.00%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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