Several universal approximation and universal representation results are known for non Boolean multi valued logics such as fuzzy logics In this paper we show that similar results can be proven for multi valued Boolean logics as well Introduction The study of Boolean algebras started when G Boole con sidered the simplest Boolean algebra the two valued algebra B f g ffalse trueg In this algebra t...

A subsetA of a Boolean algebra B is said to be (n,m)reaped if there is a partition of unity P ⊂ B of size n such that |{b ∈ P : b∧a 6= ∅}| ≥ m for all a ∈ A. The reaping number rn,m(B) of a Boolean algebra B is the minimum cardinality of a set A ⊂ B\ {0} such which cannot be (n,m)-reaped. It is shown that, for each n ∈ ω, there is a Boolean algebra B such that rn+1,2(B) 6= rn,2(B). Also, {rn,m(...

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characte...

We generalize to universal algebra concepts originating from λ-calculus and programming to prove a new result on the lattice λT of λ-theories, and a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. In this paper we introduce the class of Church algebras (which includes all Boolean algebras, combinatory algebras, rings with unit a...

We prove the following result about the degree spectrum of the atom relation on a computable Boolean algebra. Let C be a computable Boolean algebra with infinitely many atoms and a be the Turing degree of the atom relation of C. If d is a c.e. degree such that a′′′ ≤T d′′′, then there is a computable copy of C where the atom relation has degree d. In particular, for every high3 c.e. degree d, a...

The degree of a structure si is the Turing degree of its open diagram £»(j/) , coded as a subset of a>. Implicit in the definition is a particular presentation of the structure; the degree is not an isomorphism invariant. We prove that if a Boolean algebra si has a copy of low 2 degree, then there is a recursive Boolean algebra 33 which is isomorphic to si . This builds on work of Downey and Jo...

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtain that the fixed point set of additive derivations is still an MV-algebra. Also, we study Boolean additive derivations and their adjoint derivations. In particular, we get that the fixed point set of Boolean addition derivations an...

The Forward Problem (FB) of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X) = 0 where f(X): B n → B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB) of Boolean equations aims to reconstruct the equation f (X) = 0 given the set of solutions and hence to verify the correctness...

Flaminio and Montagna (2008) enlarged the language of MV-algebras by a unary operation σ, called internal state or a state operator, equationally defined so as to preserve the basic properties of a state in its usual meaning. The resulting class of MV-algebras is called state MV-algebras. Jenča (2007) and Vetterlein (2008), using different approaches, represented MV-algebras through the quotien...