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Paper Abstract and Keywords
Presentation 2012-06-21 11:25
Recursive and non recursive formulas in finitism
Eiichi Tanaka (Kobe Univ.) COMP2012-16
Abstract (in Japanese) (See Japanese page) 
(in English) This report shows that the diagonalization in the set of all finite length unary functions (formulas) produces a non-finite length function (formula) under a strict finitism. This fact gives a chance to review several established theories such as the first incompleteness theorem, the diagonal theorem, a typical proof of the halting problem of a Turing machine, and so on. A finitism without the concept of infinity does not cover the Gödel’s world.
Keyword (in Japanese) (See Japanese page) 
(in English) The first incompleteness theorem / Recursive function theory / Finitism / Diagonalization / Halting problem / / /  
Reference Info. IEICE Tech. Rep., vol. 112, no. 93, COMP2012-16, pp. 33-40, June 2012.
Paper # COMP2012-16 
Date of Issue 2012-06-14 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee COMP  
Conference Date 2012-06-21 - 2012-06-21 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2012-06-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Recursive and non recursive formulas in finitism 
Sub Title (in English)  
Keyword(1) The first incompleteness theorem  
Keyword(2) Recursive function theory  
Keyword(3) Finitism  
Keyword(4) Diagonalization  
Keyword(5) Halting problem  
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1st Author's Name Eiichi Tanaka  
1st Author's Affiliation Kobe University (Kobe Univ.)
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Speaker Author-1 
Date Time 2012-06-21 11:25:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # COMP2012-16 
Volume (vol) vol.112 
Number (no) no.93 
Page pp.33-40 
#Pages
Date of Issue 2012-06-14 (COMP) 


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