Schuster, PM (2013) Induction in Algebra: a First Case Study. Logical Methods in Computer Science, 9 (3). 20. ? - ? (19). ISSN 1860-5974
Abstract
Many a concrete theorem of abstract algebra admits a short and elegant proof by contradiction but with Zorn's Lemma (ZL). A few of these theorems have recently turned out to follow in a direct and elementary way from the Principle of Open Induction distinguished by Raoult. The ideal objects characteristic of any invocation of ZL are eliminated, and it is made possible to pass from classical to intuitionistic logic. If the theorem has finite input data, then a finite partial order carries the required instance of induction, which thus is constructively provable. A typical example is the well-known theorem ``every nonconstant coefficient of an invertible polynomial is nilpotent''.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013 Schuster P.M. Creative Commons Creative Commons License Deed Attribution-NoDerivs 2.0 Generic (CC BY-ND 2.0) |
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: | 21 Oct 2013 10:48 |
Last Modified: | 18 Jan 2018 00:14 |
Published Version: | http://www.lmcs-online.org/index.php |
Status: | Published |
Publisher: | International Federation of Computational Logic |
Identification Number: | 10.2168/LMCS-9(3:20)2013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:76499 |