Rathjen, M (2010) Investigations of subsystems of second order arithmetic and set theory in strength between Pi-1-1-CA and delta-1-2-CA+BI: part I. In: Ways of proof theory. Walter de Gruyter , 363 - 440. ISBN 978-3-86838-087-3
Abstract
This paper is the rst of a series of two. It contains proof{theoretic investigations on subtheories of second order arithmetic and set theory. Among the principles on which these theories are based one nds autonomously iterated positive and monotone inductive de ni- tions, 1 1 trans nite recursion, 1 2 trans nite recursion, trans nitely iterated 1 1 dependent choices, extended Bar rules for provably de nable well-orderings as well as their set-theoretic counterparts which are based on extensions of Kripke-Platek set theory. This rst part intro- duces all the principles and theories. It provides lower bounds for their strength measured in terms of the amount of trans nite induction they achieve to prove. In other words, it determines lower bounds for their proof-theoretic ordinals which are expressed by means of ordinal representation systems. The second part of the paper will be concerned with ordinal analysis. It will show that the lower bounds established in the present paper are indeed sharp, thereby providing the proof-theoretic ordinals. All the results were obtained more then 20 years ago (in German) in the author's PhD thesis [43] but have never been published before, though the thesis received a review (MR 91m#03062). I think it is high time it got published.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2010, De Gruyter. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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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: | 09 Oct 2014 17:27 |
Last Modified: | 15 Nov 2014 09:31 |
Published Version: | http://www.degruyter.com/view/books/9783110324907/... |
Status: | Published |
Publisher: | Walter de Gruyter |
Identification Number: | 10.1515/9783110324907.363 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:76751 |