New Trends in Quantum Structures:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Mathematics and Its Applications
516 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 Wahrscheinlichkeitsrechnung 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 experimentally 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 542 p) |
| ISBN: | 9789401724227 9789048155255 |
| DOI: | 10.1007/978-94-017-2422-7 |
Internformat
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| 500 | |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 Wahrscheinlichkeitsrechnung 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 experimentally 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 | ||
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Datensatz im Suchindex
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| author | Dvurečenskij, Anatolij 1949- |
| author_GND | (DE-588)172681979 |
| author_facet | Dvurečenskij, Anatolij 1949- |
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| author_sort | Dvurečenskij, Anatolij 1949- |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-2422-7 |
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| indexdate | 2024-07-10T01:21:15Z |
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| isbn | 9789401724227 9789048155255 |
| language | English |
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| spelling | Dvurečenskij, Anatolij 1949- Verfasser (DE-588)172681979 aut New Trends in Quantum Structures by Anatolij Dvurečenskij, Sylvia Pulmannová Dordrecht Springer Netherlands 2000 1 Online-Ressource (XVI, 542 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 516 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 Wahrscheinlichkeitsrechnung 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 experimentally 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 Mathematics Algebra Logic, Symbolic and mathematical Quantum theory Order, Lattices, Ordered Algebraic Structures Applications of Mathematics Mathematical Logic and Foundations Quantum Physics Mathematik Quantentheorie Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Mathematik (DE-588)4037944-9 s 1\p DE-604 Mathematisches Modell (DE-588)4114528-8 s 2\p DE-604 Pulmannová, Sylvia Sonstige oth Mathematics and Its Applications 516 (DE-604)BV008163334 516 https://doi.org/10.1007/978-94-017-2422-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dvurečenskij, Anatolij 1949- New Trends in Quantum Structures Mathematics and Its Applications Mathematics Algebra Logic, Symbolic and mathematical Quantum theory Order, Lattices, Ordered Algebraic Structures Applications of Mathematics Mathematical Logic and Foundations Quantum Physics Mathematik Quantentheorie Mathematik (DE-588)4037944-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4114528-8 (DE-588)4047992-4 |
| title | New Trends in Quantum Structures |
| title_auth | New Trends in Quantum Structures |
| title_exact_search | New Trends in Quantum Structures |
| title_full | New Trends in Quantum Structures by Anatolij Dvurečenskij, Sylvia Pulmannová |
| title_fullStr | New Trends in Quantum Structures by Anatolij Dvurečenskij, Sylvia Pulmannová |
| title_full_unstemmed | New Trends in Quantum Structures by Anatolij Dvurečenskij, Sylvia Pulmannová |
| title_short | New Trends in Quantum Structures |
| title_sort | new trends in quantum structures |
| topic | Mathematics Algebra Logic, Symbolic and mathematical Quantum theory Order, Lattices, Ordered Algebraic Structures Applications of Mathematics Mathematical Logic and Foundations Quantum Physics Mathematik Quantentheorie Mathematik (DE-588)4037944-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Mathematics Algebra Logic, Symbolic and mathematical Quantum theory Order, Lattices, Ordered Algebraic Structures Applications of Mathematics Mathematical Logic and Foundations Quantum Physics Mathematik Quantentheorie Mathematisches Modell |
| url | https://doi.org/10.1007/978-94-017-2422-7 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT dvurecenskijanatolij newtrendsinquantumstructures AT pulmannovasylvia newtrendsinquantumstructures |