Two General Results on Intuitionistic Bounded Theories

✍ Scribed by Fernando Ferreira

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 560 KB
• Volume: 45
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19990450310

✦ Synopsis

Abstract

We study, within the framework of intuitionistic logic, two well‐known general results of (classical logic) bounded arithmetic. Firstly, Parikh's theorem on the existence of bounding terms for the provably total functions. Secondly, the result which states that adding the scheme of bounded collection to (suitable) bounded theories does not yield new II~2~ consequences.