New Trends in Quantum Structures

Anatolij Dvurecenskij, Sylvia Pulmannová (Autoren)

Buch | Softcover

542 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2000
Springer (Verlag)
978-90-481-5525-5 (ISBN)

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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.

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.

Erscheint lt. Verlag	15.12.2010
Reihe/Serie	Mathematics and Its Applications ; 516
Zusatzinfo	XVI, 542 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	90-481-5525-8 / 9048155258
ISBN-13	978-90-481-5525-5 / 9789048155255
Zustand	Neuware