Spaces of Abstract Events

被引：7
|
作者：
Chajda, Ivan [1 ]
Laenger, Helmut [2 ]
机构：
[1] Palacky Univ, Fac Sci, Dept Algebra & Geometry, Olomouc 77146, Czech Republic
[2] Vienna Univ Technol, Inst Discrete Math & Geometry, Fac Math & Geoinformat, A-1040 Vienna, Austria
来源：
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2013年 / 52卷 / 06期
关键词：
Numerical event; Abstract event; Orthomodular poset; Effect algebra; State; Full set of states; Antitone involution; Sectionally antitone involutions; Orthomodular lattice; EFFECT ALGEBRAS; PROBABILITIES;
D O I：
10.1007/s10773-012-1275-7
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We generalize the concept of a space of numerical events in such a way that this generalization corresponds to arbitrary orthomodular posets whereas spaces of numerical events correspond to orthomodular posets having a full set of states. Moreover, we show that there is a natural one-to-one correspondence between orthomodular posets and certain posets with sectionally antitone involutions. Finally, we characterize orthomodular lattices among orthomodular posets.
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页码：1818 / 1824
页数：7
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