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Dynamic ordinal analysis

Arnold Beckmann Orcid Logo

Archive for Mathematical Logic, Volume: 42, Issue: 4, Pages: 303 - 334

Swansea University Author: Arnold Beckmann Orcid Logo

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DOI (Published version): 10.1007/s00153-002-0169-4

Abstract

Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals - they will be sets of number theoretic functions measuring the amount of Π b 1 (α) order induction available in a theory. We will compare order induc...

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Published in: Archive for Mathematical Logic
ISSN: 0933-5846 1432-0665
Published: Springer 2002
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URI: https://cronfa.swan.ac.uk/Record/cronfa1701
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spelling 2013-10-17T11:45:51.6797797 v2 1701 2011-10-01 Dynamic ordinal analysis 1439ebd690110a50a797b7ec78cca600 0000-0001-7958-5790 Arnold Beckmann Arnold Beckmann true false 2011-10-01 MACS Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals - they will be sets of number theoretic functions measuring the amount of Π b 1 (α) order induction available in a theory. We will compare order induction to successor induction over weak theories. We will compute dynamic ordinals of the bounded arithmetic theories Σ b n (α)-LmIND for m=n and m=n+1, n≥0 . Different dynamic ordinals lead to separation. Therefore, we will obtain several separation results between these relativized theories. We will generalize our results to arbitrary languages extending the language of Peano arithmetic. Journal Article Archive for Mathematical Logic 42 4 303 334 Springer 0933-5846 1432-0665 19 12 2002 2002-12-19 10.1007/s00153-002-0169-4 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2013-10-17T11:45:51.6797797 2011-10-01T00:00:00.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Arnold Beckmann 0000-0001-7958-5790 1
title Dynamic ordinal analysis
spellingShingle Dynamic ordinal analysis
Arnold Beckmann
title_short Dynamic ordinal analysis
title_full Dynamic ordinal analysis
title_fullStr Dynamic ordinal analysis
title_full_unstemmed Dynamic ordinal analysis
title_sort Dynamic ordinal analysis
author_id_str_mv 1439ebd690110a50a797b7ec78cca600
author_id_fullname_str_mv 1439ebd690110a50a797b7ec78cca600_***_Arnold Beckmann
author Arnold Beckmann
author2 Arnold Beckmann
format Journal article
container_title Archive for Mathematical Logic
container_volume 42
container_issue 4
container_start_page 303
publishDate 2002
institution Swansea University
issn 0933-5846
1432-0665
doi_str_mv 10.1007/s00153-002-0169-4
publisher Springer
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals - they will be sets of number theoretic functions measuring the amount of Π b 1 (α) order induction available in a theory. We will compare order induction to successor induction over weak theories. We will compute dynamic ordinals of the bounded arithmetic theories Σ b n (α)-LmIND for m=n and m=n+1, n≥0 . Different dynamic ordinals lead to separation. Therefore, we will obtain several separation results between these relativized theories. We will generalize our results to arbitrary languages extending the language of Peano arithmetic.
published_date 2002-12-19T12:07:40Z
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score 10.958922

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