On partially conservative sentences and interpretability
Per Lindström · Proceedings of the American Mathematical Society · 1984
A sentence φ \varphi is Γ \Gamma -conservative over T T if T + φ ⊢ ψ T + \varphi \vdash \psi implies T ⊢ ψ T \vdash \psi for every ψ ∈ Γ \psi \in \Gamma . In §1 this concept for Γ = ∑ n + 1 0 \Gamma = \sum _{n + 1}^0 and ∏ n + 1 0 \prod _{n + 1}^0 is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic.