02999nmm a2200385 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002700139245010800166250001700274260004800291300003200339505029800371653002400669653002000693653002800713653002300741653003900764653003200803653002000835653001200855653005000867653003300917700003400950710003400984041001901018989003801037490003701075856007201112082001101184520141801195EB000722549EBX0100000000000000057563100000000000000.0cr|||||||||||||||||||||140122 ||| eng a97894017242271 aDvurecenskij, Anatolij00aNew Trends in Quantum StructureshElektronische Ressourcecby Anatolij Dvurecenskij, Sylvia Pulmannová a1st ed. 2000 aDordrechtbSpringer Netherlandsc2000, 2000 aXVI, 542 pbonline resource0 a1 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 aApplied mathematics aQuantum Physics aEngineering mathematics aMathematical logic aMathematical Logic and Foundations aApplications of Mathematics aQuantum physics aAlgebra aOrder, Lattices, Ordered Algebraic Structures aOrdered algebraic structures1 aPulmannová, Sylviae[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aMathematics and Its Applications uhttps://doi.org/10.1007/978-94-017-2422-7?nosfx=yxVerlag3Volltext0 a511.33 aD. 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