On the set representation of an orthomodular poset

John Harding, and Pavel Pták. "On the set representation of an orthomodular poset." Colloquium Mathematicae 89.2 (2001): 233-240. <http://eudml.org/doc/283819>.

@article{JohnHarding2001,
abstract = {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.},
author = {John Harding, Pavel Pták},
journal = {Colloquium Mathematicae},
keywords = {orthomodular poset; Boolean algebra; state; set representation},
language = {eng},
number = {2},
pages = {233-240},
title = {On the set representation of an orthomodular poset},
url = {http://eudml.org/doc/283819},
volume = {89},
year = {2001},
}

TY - JOUR
AU - John Harding
AU - Pavel Pták
TI - On the set representation of an orthomodular poset
JO - Colloquium Mathematicae
PY - 2001
VL - 89
IS - 2
SP - 233
EP - 240
AB - 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.
LA - eng
KW - orthomodular poset; Boolean algebra; state; set representation
UR - http://eudml.org/doc/283819
ER -