In the present paper we study the following problem: how to construct a coherent orthoalgebra which has only a finite number of elements, but at the same time does not admit a bivaluation (i.e., a morphism with a codomain being an orthoalgebra with just two elements). This problem is important in the perspective of Bell-Kochen-Specker theory, since one can associate such an orthoalgebra to every saturated noncolorable finite configuration of projective lines. The first result obtained in this paper provides a general method for constructing finite orthoalgebras. This method is then applied to obtain a new infinite family of finite coherent orthoalgebras that do not admit bivaluations. The corresponding proof is combinatorial and yields a description of the groups of symmetries for these orthoalgebras.
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February 2006
Research Article|
February 28 2006
New families of finite coherent orthoalgebras without bivaluations
Artur E. Ruuge;
Artur E. Ruuge
Department of Quantum Statistics and Field Theory, Faculty of Physics,
Moscow State University
, Vorobyovy Gory 119899 Moscow, Russia
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Freddy Van Oystaeyen
Freddy Van Oystaeyen
Department of Mathematics and Computer Science,
University of Antwerp
, Middelheim Campus Building G, Middelheimlaan 1, B-2020 Antwerp, Belgium
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J. Math. Phys. 47, 022108 (2006)
Article history
Received:
October 12 2005
Accepted:
January 11 2006
Citation
Artur E. Ruuge, Freddy Van Oystaeyen; New families of finite coherent orthoalgebras without bivaluations. J. Math. Phys. 1 February 2006; 47 (2): 022108. https://doi.org/10.1063/1.2171691
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