# On Partially Conservative Sentences and Interpretability

Per Lindström
Proceedings of the American Mathematical Society
Vol. 91, No. 3 (Jul., 1984), pp. 436-443
DOI: 10.2307/2045318
Stable URL: http://www.jstor.org/stable/2045318
Page Count: 8

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## Abstract

A sentence φ is Γ-conservative over T if $T + \varphi \vdash \psi$ implies $T \vdash \psi$ for every ψ ∈ Γ. In $\S1$ this concept for Γ = Σ0 n + 1 and Π0 n + 1 is investigated. In $\S2$ results from $\S1$ are applied to interpretability in theories containing arithmetic.

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