A Note on Iterated Consistency and Infinite Proofs
Abstract
Schmerl and Beklemishev's work on iterated reflection achieves two aims: It introduces the important notion of -ordinal, characterizing the -theorems of a theory in terms of transfinite iterations of consistency; and it provides an innovative calculus to compute the -ordinals for a range of theories. The present note demonstrates that these achievements are independent: We read off -ordinals from a Sch\"utte-style ordinal analysis via infinite proofs, in a direct and transparent way.
Cite
@article{arxiv.1709.01540,
title = {A Note on Iterated Consistency and Infinite Proofs},
author = {Anton Freund},
journal= {arXiv preprint arXiv:1709.01540},
year = {2018}
}
Comments
This is a pre-print (before peer-review) of an article published in the Archive for Mathematical Logic. The final authenticated version is available online at https://doi.org/10.1007/s00153-018-0639-y. It can also be accessed via https://rdcu.be/2YJI (view only). Note that the journal version contains some improvements over the present pre-print