Abstract
We study the [Formula: see text]-soundness spectra of theories. Given a recursively enumerable extension [Formula: see text] of [Formula: see text], [Formula: see text] is defined as the set of all 2-ptykes on which [Formula: see text] is correct about well foundedness. This is a measure of how close [Formula: see text] is to being [Formula: see text]-sound. We carry out a proof-theoretic classification of theories according to [Formula: see text], as well as a characterization of the sets of the form [Formula: see text]. Many of the results generalize to [Formula: see text] greater than 3. This article is part of the theme issue 'Modern perspectives in Proof Theory'.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
