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arXiv · 1604.08705

The logic of Turing progressions

Eduardo Hermo Reyes·Joost J. Joosten
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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 arithmetically sound and complete for a natural interpretation, named the \emph{Formalized Turing progressions} (FTP) interpretation.

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BibTeXRIS

Eduardo Hermo Reyes, Joost J. Joosten. 2017-09-13. The logic of Turing progressions. https://doi.org/10.1215/00294527-2019-0037

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