New Families of Finite Coherent Orthoalgebras without Bivaluations

Details New Families of Finite Coherent Orthoalgebras without Bivaluations New Families of Finite Coherent Orthoalgebras without Bivaluations

2009-06-15

arxiv.org/abs/0906.2687v1

J. Math. Phys. 47 (2006), no. 2, 022108, 32 pp

Physics

Quantum Physics

Scientific paper

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 non-colorable 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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