Representative properties of the quasi-ordered set
Representing free Boolean algebras
Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra...
Representing lattices by homotopy groups of graphs
In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.
Representing real numbers in denumerable Boolean algebras
Representing Upper Probability Measures over Rational Lukasiewicz Logic.
Residual implications and co-implications from idempotent uninorms
This paper is devoted to the study of implication (and co-implication) functions defined from idempotent uninorms. The expression of these implications, a list of their properties, as well as some particular cases are studied. It is also characterized when these implications satisfy some additional properties specially interesting in the framework of implication functions, like contrapositive symmetry and the exchange principle.
RESIDUATION IN SEMIGROUPS OF PRE-CLOSURES.
Residuation in twist products and pseudo-Kleene posets
M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication....
Residuation Theory (Book Review by R. McFadden.
Restricted ideals and the groupability property. Tools for temporal reasoning
In the field of automatic proving, the study of the sets of prime implicants or implicates of a formula has proven to be very important. If we focus on non-classical logics and, in particular, on temporal logics, such study is useful even if it is restricted to the set of unitary implicants/implicates [P. Cordero, M. Enciso, and I. de Guzmán: Structure theorems for closed sets of implicates/implicants in temporal logic. (Lecture Notes in Artificial Intelligence 1695.) Springer–Verlag, Berlin 1999]....
Resultats sur la comparaison des types d΄ordres
Reticulation of a 0-distributive Lattice
A congruence relation on a 0-distributive lattice is defined such that the quotient lattice is a distributive lattice and the prime spectrum of and of are homeomorphic. Also it is proved that the minimal prime spectrum (maximal spectrum) of is homeomorphic with the minimal prime spectrum (maximal spectrum) of .
Retract extensions of ordered sets.
Retract varieties of lattice ordered groups
Retractive MV-algebras.
Retracts and Q-independence
A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a₁,a₂,...,aₙ of X implies f(p(a₁),p(a₂),...,p(aₙ)) = g(p(a₁),p(a₂),...,p(aₙ)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). We investigate Q-independent subsets of algebras which have a retraction in their set of term functions.
Retracts of abelian cyclically ordered groups
Retracts of abelian lattice ordered groups
Retracts of abelian multilattice groups
Richesses du centre d'un espace vectoriel réticulé.