On the Σ01-conservativity of Σ01-completeness

Albert Visser

doi:10.1305/ndjfl/1093635927

On the Σ⁰₁-conservativity of Σ⁰₁-completeness

Albert Visser^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	554-561
Number of pages	8
Journal	Notre Dame Journal of Formal Logic
Volume	32
Issue number	4
DOIs	https://doi.org/10.1305/ndjfl/1093635927
Publication status	Published - 1991

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title = "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.",

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AB - 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.

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JF - Notre Dame Journal of Formal Logic

IS - 4

ER -

On the Σ⁰₁-conservativity of Σ⁰₁-completeness

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