New Trends in Quantum Structures

1. Auflage. Softcover version of original hardcover Auflage 2000
ISBN: 978-90-481-5525-5
Verlag: Springer Netherlands

Buch, Englisch, Band 516, 542 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 838 g

Reihe: Mathematics and Its Applications

D. Hilbert, in his famous program, formulated many open mathematical problems which were stimulating for the development of mathematics and a fruitful source of very deep and fundamental ideas. During the whole 20th century, mathematicians and specialists in other fields have been solving problems which can be traced back to Hilbert's program, and today there are many basic results stimulated by this program. It is sure that even at the beginning of the third millennium, mathematicians will still have much to do. One of his most interesting ideas, lying between mathematics and physics, is his sixth problem: To find a few physical axioms which, similar to the axioms of geometry, can describe a theory for a class of physical events that is as large as possible. We try to present some ideas inspired by Hilbert's sixth problem and give some partial results which may contribute to its solution. In the Thirties the situation in both physics and mathematics was very interesting. A.N. Kolmogorov published his fundamental work Grundbegriffe der Wahrschein­ lichkeitsrechnung in which he, for the first time, axiomatized modern probability theory. From the mathematical point of view, in Kolmogorov's model, the set L of ex­ perimentally verifiable events forms a Boolean a-algebra and, by the Loomis-Sikorski theorem, roughly speaking can be represented by a a-algebra S of subsets of some non-void set n.

Zielgruppe

Research

Autoren/Hrsg.

Pulmannová, Sylvia

Dvurecenskij, Anatolij

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

1 D-posets and Effect Algebras.- 2 MV-algebras and QMV-algebras.- 3 Quotients of Partial Abelian Monoids.- 4 Tensor Product of D-Posets and Effect Algebras.- 5 BCK-algebras.- 6 BCK-algebras in Applications.- 7 Loomis-Sikorski Theorems for MV-algebras and BCK-algebras.- Index of Symbols.