On the set representation of an orthomodular poset

• Autorzy: John Harding , Pavel Pták
• Języki publikacji: EN

Abstrakty

EN

Let P be an orthomodular poset and let B be a Boolean subalgebra of P. A mapping s:P → ⟨0,1⟩ is said to be a centrally additive B-state if it is order preserving, satisfies s(a') = 1 - s(a), is additive on couples that contain a central element, and restricts to a state on B. It is shown that, for any Boolean subalgebra B of P, P has an abundance of two-valued centrally additive B-states. This answers positively a question raised in [13, Open question, p. 13]. As a consequence one obtains a somewhat better set representation of orthomodular posets and a better extension theorem than in [2, 12, 13]. Further improvement in the Boolean vein is hardly possible as the concluding example shows.

Kategorie tematyczne

• 06C15: Complemented lattices, orthocomplemented lattices and posets
• 81P10: Logical foundations of quantum mechanics; quantum logic

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 2
• Strony: 233-240

Daty

wydano

2001

Twórcy

autor

John Harding

• Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, U.S.A.

autor

Pavel Pták

• Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 16627 Praha 6, Czech Republic

Identyfikatory

DOI

10.4064/cm89-2-8