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Proof theory and Martin-Löf Type Theory

Anton Setzer Orcid Logo

One Hundred Years of Intuitionism (1907–2007), Pages: 257 - 279

Swansea University Author: Anton Setzer Orcid Logo

DOI (Published version): 10.1007/978-3-7643-8653-5_16

Abstract

In this article an overview over the work of the author on developing proof theoretic strong extensions of Martin-Loef Type Theory including precise proof theoretic bounds is given. It presents the first publication of the proof theoretically strongest known extensions of Martin-Loef Type Theory, na...

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Published in: One Hundred Years of Intuitionism (1907–2007)
Published: Birkhäuser 2008
Online Access: http://www.springerlink.com/content/lw112klq80w11636/
URI: https://cronfa.swan.ac.uk/Record/cronfa12
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spelling 2015-05-17T17:33:21.9529114 v2 12 2011-10-01 Proof theory and Martin-Löf Type Theory 5f7695285397f46d121207120247c2ae 0000-0001-5322-6060 Anton Setzer Anton Setzer true false 2011-10-01 SCS In this article an overview over the work of the author on developing proof theoretic strong extensions of Martin-Loef Type Theory including precise proof theoretic bounds is given. It presents the first publication of the proof theoretically strongest known extensions of Martin-Loef Type Theory, namely the hyper-Mahlo Universe, the hyper-alpha-Mahlo universe, the autononomous Mahlo universe and the Pi_3-reflecting universe. This is part of a proof theoretic program in developing proof theoretic as strong as possible constructive theories in order to obtain a constructive underpinning of strong classical theories with a full proof theoretic analysis. Book chapter One Hundred Years of Intuitionism (1907–2007) 257 279 Birkhäuser 9 11 2008 2008-11-09 10.1007/978-3-7643-8653-5_16 http://www.springerlink.com/content/lw112klq80w11636/ In One hundred years of intuitionism (1907 -- 2007) (ed. Atten, M. v.; Boldini, P.; Bourdeau, M.; Heinzmann, G.) COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2015-05-17T17:33:21.9529114 2011-10-01T00:00:00.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Anton Setzer 0000-0001-5322-6060 1 0009213-18052015010232.pdf setzerProofTheoryAndMartinLoefTypeTheory.pdf 2015-05-17T17:33:12.8730000 Output 264302 application/pdf Accepted Manuscript true 2015-05-17T17:33:12.0000000 false
title Proof theory and Martin-Löf Type Theory
spellingShingle Proof theory and Martin-Löf Type Theory
Anton Setzer
title_short Proof theory and Martin-Löf Type Theory
title_full Proof theory and Martin-Löf Type Theory
title_fullStr Proof theory and Martin-Löf Type Theory
title_full_unstemmed Proof theory and Martin-Löf Type Theory
title_sort Proof theory and Martin-Löf Type Theory
author_id_str_mv 5f7695285397f46d121207120247c2ae
author_id_fullname_str_mv 5f7695285397f46d121207120247c2ae_***_Anton Setzer
author Anton Setzer
author2 Anton Setzer
format Book chapter
container_title One Hundred Years of Intuitionism (1907–2007)
container_start_page 257
publishDate 2008
institution Swansea University
doi_str_mv 10.1007/978-3-7643-8653-5_16
publisher Birkhäuser
college_str Faculty of Science and Engineering
hierarchytype
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
url http://www.springerlink.com/content/lw112klq80w11636/
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description In this article an overview over the work of the author on developing proof theoretic strong extensions of Martin-Loef Type Theory including precise proof theoretic bounds is given. It presents the first publication of the proof theoretically strongest known extensions of Martin-Loef Type Theory, namely the hyper-Mahlo Universe, the hyper-alpha-Mahlo universe, the autononomous Mahlo universe and the Pi_3-reflecting universe. This is part of a proof theoretic program in developing proof theoretic as strong as possible constructive theories in order to obtain a constructive underpinning of strong classical theories with a full proof theoretic analysis.
published_date 2008-11-09T03:02:54Z
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