On the $\Sigma^0_1$-conservativity of $\Sigma^0_1$-completeness.
Albert Visser · Notre Dame Journal of Formal Logic · 1991
In this paper we show that /Δ o + Ωi verifies the sentential Σ?conservativity of schematical, sentential Σ?-completeness.(This means that for any finite set of Σ?-sentences 5 we can prove in /Δ o + Ωi that the statement expressing the completeness of S w.r.t.7Δ 0 + Ωi is conservative over 7Δ 0 + Ω! w.r.t.Σi-sentences.)Some consequences are discussed.We formulate a system of provability logic based on the verifiable sentential Σ?-conservativity of schematical, sentential Σ?-completeness.