0100491853

open access

Accepted Manuscript

On the conservation results for local reflection principles

English (英語)

Journal of Logic and Computation

exad076

Oxford University Press

2024-01-04

2025-01-04

For a class Γ of formulas, Γ local reflection principle Rfn_Γ(T) for a theory T of arithmetic is a scheme formalizing the Γ-soundness of T⁠. Beklemishev (1997, Theoria, 63, 139–146) proved that for every Γ ∈ {Σₙ,Σₙ₋₁ | n ≥ 1}⁠, the full local reflection principle Rfn(T) is Γ-conservative over T + Rfn_Γ(T)⁠. We firstly generalize the conservation theorem to nonstandard provability predicates: we prove that the second condition D2 of the derivability conditions is a sufficient condition for the conservation theorem to hold. We secondly investigate the conservation theorem in terms of Rosser provability predicates. We construct Rosser predicates for which the conservation theorem holds and Rosser predicates for which the theorem does not hold.

Conservation theorem

学術雑誌論文

This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of Logic and Computation following peer review. The version of record Haruka Kogure, Taishi Kurahashi, On the conservation results for local reflection principles, Journal of Logic and Computation, 2024;, exad076. is available online at:https://doi.org/10.1093/logcom/exad076.