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References (13)
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Mathematical system of potential infinities (II) - formal systems of logical basisKybernetes, 37
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Yi Lin, Wujia Zhu, N. Gong, Guoping Du (2008)
Systemic yoyo structure in human thoughts and the fourth crisis in mathematicsKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Cauchy theater phenomenon in diagonal method and test principle of finite positional differencesKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
The inconsistency of countable infinite setsKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
The inconsistency of the natural number systemKybernetes, 37
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10.1108/03684920810863435
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Modern system of mathematics and special Cauchy theater in its theoretical foundationKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Descriptive definitions of potential and actual infinitiesKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Mathematical system of potential infinities (I) - preparationKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Inconsistency of uncountable infinite sets under ZFC frameworkKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Wide-range co-existence of potential and actual infinities in modern mathematicsKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
New Berkeley paradox in the theory of limitsKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Modern system of mathematics and a pair of hidden contradictions in its foundationKybernetes, 37
- Publisher
- Emerald Publishing
- Copyright
- Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
- ISSN
- 0368-492X
- DOI
- 10.1108/03684920810863499
- Publisher site
- See Article on Publisher Site
Abstract
Purpose – This paper is the third part of the effort to resolve the following two problems, which urgently need an answer: how can an appropriate theoretical foundation be chosen for modern mathematics and computer science? And, under what interpretations can modern mathematics and the theory of computer science be kept as completely as possible? Design/methodology/approach – The paper is a conceptual discussion of the metatheory. Findings – The paper establishes the metatheory of the logical foundation for the mathematical system of potential infinities. Originality/value – The authors prove the relevant results on the reliability and the completeness of the logical system.
Journal
Kybernetes – Emerald Publishing
Published: Apr 11, 2008
Keywords: Cybernetics; Set theory