A characterization of Boolean algebra

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...

Free Boolean Algebra

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

An Algebra of Boolean Processes

This work has been motivated by the study of the S=R models which allow to represent systems as a set of communicating state machines cooperating through a shared memory. We show that S=R models can be expressed in terms of a process algebra called Boolean SCCS which is a special case of Milner's SCCS, in the sense that the actions are elements of some boolean algebra. We deene for Boolean SCCS...