New trends in quantum structures
New trends in quantum structures
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DOI：
10.1007/978-94-017-2422-7
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Dvurecenskij;S. Pulmannová
中科院分区：
文献类型：
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作者：
A. Dvurecenskij;S. Pulmannová
D.希尔伯特，在他著名的计划，制定了许多开放的数学问题，刺激了数学的发展和富有成效的来源非常深刻和基本的想法。在整个世纪，数学家和其他领域的专家一直在解决可以追溯到希尔伯特纲领的问题，今天有许多基本结果是由这个纲领激发的。可以肯定的是，即使在第三个千年开始时，数学家们仍将有许多工作要做。他的一个最有趣的想法，躺在数学和物理，是他的第六个问题：找到几个物理公理，类似于几何公理，可以描述一个理论的一类物理事件是尽可能大的。本文试图从Hilbert第六问题出发，提出一些新的思路，并给出一些可能有助于解决该问题的部分结果。在三十年代的情况下，在物理和数学是非常有趣的。安哥洛夫出版了他的基本工作Grundbegriffe之Wahrschein lichkeitsrechnung中，他第一次，公理化现代概率论。从数学的观点来看，在柯尔莫哥洛夫模型中，实验可验证事件的集合L形成布尔a-代数，并且通过卢米斯-西科尔斯基定理，粗略地说，可以用某个非空集合n的子集的a-代数S来表示。
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. AN 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.