English

The logic of Turing progressions

Logic 2020-11-11 v2

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.

Keywords

Cite

@article{arxiv.1604.08705,
  title  = {The logic of Turing progressions},
  author = {Eduardo Hermo Reyes and Joost J. Joosten},
  journal= {arXiv preprint arXiv:1604.08705},
  year   = {2020}
}
R2 v1 2026-06-22T13:44:15.874Z