A note on parameter free Π1-induction and restricted exponentiation

✍ Scribed by A. Cordón-Franco; A. Fernández-Margarit; F. F. Lara-Martín

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 182 KB
• Volume: 57
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.201010013

✦ Synopsis

MSC (2010) 03F30, 03H15

We characterize the sets of all Π2 and all B(Σ1 ) (= Boolean combinations of Σ1 ) theorems of IΠ - 1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ - n + 1 is conservative over IΣ - n with respect to B(Σn + 1 ) sentences cannot be extended to Πn + 2 sentences.