An algebraic version of the Strong Black Box

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2003
• Автори: Göbel, R., Wallutis, S.L.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут прикладної математики і механіки НАН України 2003
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/155695
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: An algebraic version of the Strong Black Box / R. Göbel, S.L. Wallutis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 3. — С. 7–45. — Бібліогр.: 9 назв. — англ.

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.