Carlucci, L, Mainardi, L and Rathjen, M (2019) A Note on the Ordinal Analysis of RCA0+WO(σ). In: Manea, F, Martin, B, Paulusma, D and Primiero, G, (eds.) Lecture Notes in Computer Science. Computability in Europe 2019: Computing with Foresight and Industry, 15-19 Jul 2019, Durham, UK. Springer , Cham, Switzerland , pp. 144-155. ISBN 978-3-030-22995-5
Abstract
We fill an apparent gap in the literature by giving a short and self-contained proof that the ordinal of the theory RCA0+WO(σ) is σω , for any ordinal σ satisfying ω⋅σ=σ (e.g., ωω , ωωω , ε0 ). Theories of the form RCA0+WO(σ) are of interest in Proof Theory and Reverse Mathematics because of their connections to a number of well-investigated combinatorial principles related to various subsystems of arithmetic.
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Editors: |
|
Copyright, Publisher and Additional Information: | © 2019, Springer Nature Switzerland AG. This is an author produced version of a conference paper published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
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) |
Funding Information: | Funder Grant number John Templeton Foundation (US) 60842 |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Jun 2019 15:32 |
Last Modified: | 28 Sep 2022 03:15 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/978-3-030-22996-2_13 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147185 |