Effect algebra counterexamples
Effect algebras and ring-like structures
The dichotomic physical quantities, also called propositions, can be naturally associated to maps of the set of states into the real interval [0,1]. We show that the structure of effect algebra associated to such maps can be represented by quasiring structures, which are a generalization of Boolean rings, in such a way that the ring operation of addition can be non-associative and the ring multiplication non-distributive with respect to addition. By some natural assumption on the effect algebra,...
Ein neues Axiomensystem für Boolesche Verbände.
Embedding of free Boolean algebras in complete Boolean algebras
Embeddings of quasicells of iterative algebras.
Endothéorie de Galois abstraite
Engel BCI-algebras: an application of left and right commutators
We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that...
Enlargements of Boolean algebras and Stone spaces
Enlargements without urelements
Entropic Hopf algebras and models of non-commutative logic.
Entropy on effect algebras with Riesz decomposition property II: MV-algebras
We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.
Entropy on effect algebras with the Riesz decomposition property I: Basic properties
We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
Equational Reformulations of Intuitionistic Propositional Calculus and Classical First-order Predicate Calculus
Equational spectrum of Hilbert varieties
We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.
Equational Theories of Varieties defined by P-compatible Identities of Boole'an Algebras
Errata to the article ``Topologies on quantum logics induced by measures''
Every uniformly Archimedean atomic MV-effect algebra is sharply dominating
Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.
Exhaustive zero-convergence structures on Boolean algebras
Exotic logics
Exploring the gap between linear and classical logic.