Boolean Centre of Pre A*-Algebra

132 Pre - Boolean Algebra , Ordered Dsmt and Dsm Continuous Models

When implementing the DSmT, a difficulty may arise from the possible huge dimension of hyper-power sets, which are indeed free structures. However, it is possible to reduce the dimension of these structures by involving logical constraints. In this chapter, the logical constraints will be related to a predefined order over the logical propositions. The use of such orders and their resulting log...

Centre of an algebra

Motivated by algebraic structures appearing in Rational Conformal Field Theory we study a construction associating to an algebra in a monoidal category a commutative algebra (full centre) in the monoidal centre of the monoidal category. We establish Morita invariance of this construction by extending it to module categories. As an example we treat the case of group-theoretical categories.

Ternary Boolean Algebra

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...

Subalgebras of a Finite Monadic Boolean Algebra

For a finite n-element set X, n ≥ 1, let N [X] denote the number of elements of X and let p(n) denote the number of all partitions of X. If Bn is a Boolean algebra with n atoms, let A(Bn) be the set of all atoms of Bn. It is known that there exists a bijective correspondence between the set S(Bn) of all subalgebras of Bn and the set of all partitions of A(Bn), i.e., N [S(Bn)] = p(n). The follow...