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...

In this paper new concepts countable join property, countable meet property, P–lattice and Pδ –lattice are introduced. We established that P–lattice and Pδ –lattice are measureable partial lattices and characterized partial lattices of a lattice through countable join and meet properties. We also established some interesting result on the injective property of the lattice measurable functio...

A Π1 class P is called thin if, given a subclass P ′ of P there is a clopen C with P ′ = P ∩C. Cholak, Coles, Downey and Herrmann [7] proved that a Π1 class P is thin if and only if its lattice of subclasses forms a Boolean algebra. Those authors also proved that if this boolean algebra is the free Boolean algebra, then all such think classes are automorphic in the lattice of Π1 classes under i...

We generalize to universal algebra concepts originating from lambda calculus and programming in order first to prove a new result on the lattice of λ-theories, and second a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. The interest of a systematic study of the lattice λT of λ-theories grows out of several open problems on lamb...

We discuss the relationship between the notion of independence as defined in lattice theory, matroid theory, and Boolean algebras. Collections of Boolean sub-algebras {At} are indeed endowed with the following independence relation (IB) ∩At 6= ∧ with ∧ the initial element of the Boolean algebra they belong to. However, those collections can be given several algebraic interpretations in terms of...

The algebraic structures of the genetic code are most important to obtain additional information about the semantic code and its applications. In this paper we define two dual Boolean codon lattices of the genetic code using hydrogen bond numbers and the chemical types of bases: purines and pyrimidines. The Boolean lattices reflect the role of hydrophobicity in the distribution of codon assignm...

We propose local versions of monotonicity for Boolean and pseudoBoolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are ...