Das Assoziativgesetz als Kummutativitätsaxiom in Boole'schen Zwerchverbänden.
Décompositions d'une fonction de plusieurs variables
Dedekind completions of lattices by ends
Dedekind extension of measures with values in vector lattices.
Dense extensions of a partially ordered set.
Didactical note: probabilistic conditionality in a Boolean algebra.
This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will...
Die Anwendung der Polarität auf die direkten Produktzerlegungen einer Gruppe
Die atomare Struktur topologischer Boolescher Ringe und s-beschränkter Inhalte
Die Operationen in der Klasse komplementärer Verbände
Directoids with an antitone involution
We investigate -directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids...
Discriminator varieties of Boolean algebras with residuated operators
The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated...
Disjoint refinement and related topics
Disjoint sequences in Boolean algebras
We deal with the system of all sequential convergences on a Boolean algebra . We prove that if is a sequential convergence on which is generated by a set of disjoint sequences and if is any element of , then the join exists in the partially ordered set . Further we show that each interval of is a Brouwerian lattice.
Dominating analytic families
Let A be an analytic family of sequences of sets of integers. We show that either A is dominated or it contains a continuum of almost disjoint sequences. From this we obtain a theorem by Shelah that a Suslin c.c.c. forcing adds a Cohen real if it adds an unbounded real.