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January 2020 The Logic of Turing Progressions
Eduardo Hermo Reyes, Joost J. Joosten
Notre Dame J. Formal Logic 61(1): 155-180 (January 2020). DOI: 10.1215/00294527-2019-0037

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 (FTP) interpretation.

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Eduardo Hermo Reyes. Joost J. Joosten. "The Logic of Turing Progressions." Notre Dame J. Formal Logic 61 (1) 155 - 180, January 2020. https://doi.org/10.1215/00294527-2019-0037

Information

Received: 6 December 2017; Accepted: 20 February 2019; Published: January 2020
First available in Project Euclid: 20 December 2019

zbMATH: 07196097
MathSciNet: MR4054250
Digital Object Identifier: 10.1215/00294527-2019-0037

Subjects:
Primary: 03F45
Secondary: 03F03, 03F30

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 1 • January 2020
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