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Boolean orthoposets and two-valued Jauch-Piron states

In: Tatra Mountains Mathematical Publications, vol. 3, no. 2
Josef Tkadlec
Detaily:
Rok, strany: 1993, 155 - 160
O článku:
A Boolean orthoposet is the orthoposet $P$ fulfilling the following condition: if $a\vee b=0$ then $a\bot b$. Boolean orthoposets enjoy some properties of Boolean algebras but, in some sense, they are far away of them [V. Müller, P. Pták, J. Tkadlec: Concrete quantum logics with covering properties, Internat. J. Theoret. Phys. 31 (1992), 843–854], [M. Navara, P. Pták: Almost Boolean orthomodular posets, J. Pure Appl. Algebra 60 (1989), 105–111], [J. Tkadlec: A note on distributivity in orthoposets, Demonstratio Math. 24 (1991), 343–346]. An important notion in quantum logic theory is the notion of Jauch-Piron state. [J. Jauch: Foundations of Quantum Mechanics, Addison Wesley, Reading, Mass., 1968], [C. Piron: Foundation of Quantum Physics, Benjamin, Reading, Mass., 1976], [P. Pták, S. Pulmannová: Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991], [G. T. Rüttimann.: Jauch–Piron states, J. Math. Phys. 18 (1977), 189–193]. In this paper, we show connections between Boolean orthoposets and orthoposets with a proper number of Jauch-Piron states: We demonstrate that an orthoposet with “enough” two-valued Jauch-Piron states is Boolean and, on the other hand, we give several examples of Boolean orthoposets without any two-valued Jauch-Piron state.
Ako citovať:
ISO 690:
Tkadlec, J. 1993. Boolean orthoposets and two-valued Jauch-Piron states. In Tatra Mountains Mathematical Publications, vol. 3, no.2, pp. 155-160. 1210-3195.

APA:
Tkadlec, J. (1993). Boolean orthoposets and two-valued Jauch-Piron states. Tatra Mountains Mathematical Publications, 3(2), 155-160. 1210-3195.