New Trends in Quantum Structures

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 w...

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Main Authors: Dvurecenskij, Anatolij, Pulmannová, Sylvia (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 2000, 2000
Edition:1st ed. 2000
Series:Mathematics and Its Applications
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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300 |a XVI, 542 p  |b online resource 
505 0 |a 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 
653 |a Applied mathematics 
653 |a Quantum Physics 
653 |a Engineering mathematics 
653 |a Mathematical logic 
653 |a Mathematical Logic and Foundations 
653 |a Applications of Mathematics 
653 |a Quantum physics 
653 |a Algebra 
653 |a Order, Lattices, Ordered Algebraic Structures 
653 |a Ordered algebraic structures 
700 1 |a Pulmannová, Sylvia  |e [author] 
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520 |a 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