Freund, A (2017) Slow Reflection. Annals of Pure and Applied Logic, 168 (12). pp. 2103-2128. ISSN 0168-0072
Abstract
We describe a “slow” version of the hierarchy of uniform reflection principles over Peano Arithmetic (PA). These principles are unprovable in Peano Arithmetic (even when extended by usual reflection principles of lower complexity) and introduce a new provably total function. At the same time the consistency of PA plus slow reflection is provable in PA + Con ( PA ) . We deduce a conjecture of S.-D. Friedman, Rathjen and Weiermann: Transfinite iterations of slow consistency generate a hierarchy of precisely ε 0 stages between PA and PA + Con ( PA ) (where Con ( PA ) refers to the usual consistency statement).
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017 Elsevier B.V. This is an author produced version of a paper published in Annals of Pure and Applied Logic. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Peano Arithmetic; Slow Reflection; Slow Consistency; Iterated Consistency; Consistency Strength; Fast Growing Hierarchy |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Jun 2017 11:34 |
Last Modified: | 20 Jun 2018 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.apal.2017.06.003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:117994 |