An algebraic version of the Strong Black Box
Various versions of the prediction principle called the “Black Box” are known. One of the strongest versions can be found in [EM]. There it is formulated and proven in a model theoretic way. In order to apply it to specific algebraic problems it thus has to be transformed into the desired algebraic...
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| Datum: | 2018 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/962 |
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admjournalluguniveduua-article-9622018-05-13T10:43:19Z An algebraic version of the Strong Black Box Göbel, Rüdiger Wallutis, Simone L. prediction principle, Black Box, endomorphism algebra, \(E\)-ring, \(E(R)\)-algebra, ultra-cotorsion-free module 03E75, 20K20, 20K30; 13C99 Various versions of the prediction principle called the “Black Box” are known. One of the strongest versions can be found in [EM]. There it is formulated and proven in a model theoretic way. In order to apply it to specific algebraic problems it thus has to be transformed into the desired algebraic setting. This requires intimate knowledge on model theory which often prevents algebraists to use this powerful tool. Hence we here want to present algebraic versions of this “Strong Black Box” in order to demonstrate that the proofs are straightforward and that it is easy enough to change the setting without causing major changes in the relevant proofs. This shall be done by considering three different applications where the obtained results are actually known. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/962 Algebra and Discrete Mathematics; Vol 2, No 3 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/962/491 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-05-13T10:43:19Z |
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OJS |
| language |
English |
| topic |
prediction principle Black Box endomorphism algebra \(E\)-ring \(E(R)\)-algebra ultra-cotorsion-free module 03E75 20K20 20K30; 13C99 |
| spellingShingle |
prediction principle Black Box endomorphism algebra \(E\)-ring \(E(R)\)-algebra ultra-cotorsion-free module 03E75 20K20 20K30; 13C99 Göbel, Rüdiger Wallutis, Simone L. An algebraic version of the Strong Black Box |
| topic_facet |
prediction principle Black Box endomorphism algebra \(E\)-ring \(E(R)\)-algebra ultra-cotorsion-free module 03E75 20K20 20K30; 13C99 |
| format |
Article |
| author |
Göbel, Rüdiger Wallutis, Simone L. |
| author_facet |
Göbel, Rüdiger Wallutis, Simone L. |
| author_sort |
Göbel, Rüdiger |
| title |
An algebraic version of the Strong Black Box |
| title_short |
An algebraic version of the Strong Black Box |
| title_full |
An algebraic version of the Strong Black Box |
| title_fullStr |
An algebraic version of the Strong Black Box |
| title_full_unstemmed |
An algebraic version of the Strong Black Box |
| title_sort |
algebraic version of the strong black box |
| description |
Various versions of the prediction principle called the “Black Box” are known. One of the strongest versions can be found in [EM]. There it is formulated and proven in a model theoretic way. In order to apply it to specific algebraic problems it thus has to be transformed into the desired algebraic setting. This requires intimate knowledge on model theory which often prevents algebraists to use this powerful tool. Hence we here want to present algebraic versions of this “Strong Black Box” in order to demonstrate that the proofs are straightforward and that it is easy enough to change the setting without causing major changes in the relevant proofs. This shall be done by considering three different applications where the obtained results are actually known. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/962 |
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AT gobelrudiger analgebraicversionofthestrongblackbox AT wallutissimonel analgebraicversionofthestrongblackbox AT gobelrudiger algebraicversionofthestrongblackbox AT wallutissimonel algebraicversionofthestrongblackbox |
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2025-12-02T15:47:00Z |
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2025-12-02T15:47:00Z |
| _version_ |
1850412200437481472 |