Affiliation:
1. School of Science and Technology, Meiji University, Kanagawa, Japan. makotofujiwara@meiji.ac.jp
Abstract
We formalize the primitive recursive variants of Weihrauch reduction between existence statements in finite-type arithmetic and show a meta-theorem stating that the primitive recursive Weihrauch reducibility verifiably in a classical finite-type arithmetic is identical to some formal reducibility in the corresponding (nearly) intuitionistic finite-type arithmetic for all existence statements formalized with existential free formulas. In addition, we demonstrate that our meta-theorem is applicable in some concrete examples from classical and constructive reverse mathematics.
Subject
Artificial Intelligence,Computational Theory and Mathematics,Computer Science Applications,Theoretical Computer Science
Reference23 articles.
1. The binary expansion and the intermediate value theorem in constructive reverse mathematics;Berger;Arch. Math. Logic,2019
2. E. Bishop, Foundations of Constructive Analysis, McGraw-Hill Book Co., New York–Toronto, Ont.–London, 1967.
3. Weihrauch degrees, omniscience principles and weak computability;Brattka;J. Symbolic Logic,2011
4. Effective choice and boundedness principles in computable analysis;Brattka;Bull. Symbolic Logic,2011
5. Classical consequences of continuous choice principles from intuitionistic analysis;Dorais;Notre Dame J. Form. Log.,2014
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献