The Logic of Turing Progressions

Notre Dame Journal of Formal Logic 61 (1):155-180 (2020)
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Abstract

Turing progressions arise by iteratedly adding consistency statements to a base theory. Different notions of consistency give rise to different Turing progressions. In this paper we present a logic that generates exactly all relations that hold between these different Turing progressions given a particular set of natural consistency notions. Thus, the presented logic is proven to be arithmetically sound and complete for a natural interpretation, named the formalized Turing progressions interpretation.

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Joost Joosten
Universitat de Barcelona

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References found in this work

Proof-theoretic analysis by iterated reflection.Lev D. Beklemishev - 2003 - Archive for Mathematical Logic 42 (6):515-552.
Provability algebras and proof-theoretic ordinals, I.Lev D. Beklemishev - 2004 - Annals of Pure and Applied Logic 128 (1-3):103-123.
Positive provability logic for uniform reflection principles.Lev Beklemishev - 2014 - Annals of Pure and Applied Logic 165 (1):82-105.
Iterated local reflection versus iterated consistency.Lev Beklemishev - 1995 - Annals of Pure and Applied Logic 75 (1-2):25-48.

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