On the Σ01-conservativity of Σ01-completeness

Abstract

In this paper we show that IΔ0 + Ω1 verifies the sentential Σ01- conservativity of schematical, sentential Σ01-completeness. (This means that for any finite set of Σ01-sentences S we can prove in IΔ0 + Ω1 that the statement expressing the completeness of S w.r.t. IΔ0 + Ω1 is conservative over IΔ0 + Ω1 w.r.t. Σ01-sentences.) Some consequences are discussed. We formulate a system of provability logic based on the verifiable sentential Σ01-con-servativity of schematical, sentential Σ01-completeness.