Binary consistent choice on pairs and a generalization of Konig's infinity lemma
Binary Relations-based Rough Sets – an Automated Approach
Rough sets, developed by Zdzisław Pawlak [12], are an important tool to describe the state of incomplete or partially unknown information. In this article, which is essentially the continuation of [8], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library [11]). Here we drop the classical equivalence- and tolerance-based models of rough...
Binumerability in a sequence of theories
Bipolar fuzzy finite state machines.
Birkhoff variety theorem for finite algebras
Bisemilattice-valued fuzzy sets.
BL-algebra of fractions relative to an -closed system.
BL-algebras and quantum structures
BL-algebras of basic fuzzy logic.
BL-algebras [Hajek] rise as Lindenbaum algebras from certain logical axioms familiar in fuzzy logic framework. BL-algebras are studied by means of deductive systems and co-annihilators. Duals of many theorems known to hold in MV-algebra theory remain valid for BL-algebras, too.
Blocks in homogeneous effect algebras and MV-algebras
Bolzano's infinitesimal numbers
Boolean algebras admitting a countable minimally acting group
The aim of this paper is to show that every infinite Boolean algebra which admits a countable minimally acting group contains a dense projective subalgebra.
Boolean algebras in which every chain and antichain is countable
Boolean algebras, splitting theorems, and sets
Boolean algebras with finite families of computable automorphisms.
Boolean differential operators
We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.
Boolean embeddings and hidden variables
Boolean games – Classifying strategies and omitting cardinality assumptions
Boolean matrices ... neither Boolean nor matrices
Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Boolean orthoposets---concreteness and orthocompleteness