The MacNeille completion of the poset of partial injective functions.
The maximal semigroup of quotients of a finite semilattice.
The measure algebra does not always embed
The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
The measure extension theorem for subadditive probability measures in orthomodular -continuous lattices
The Milgram non-operad
C. Berger claimed to have constructed an -operad-structure on the permutohedras, whose associated monad is exactly the Milgram model for the free loop spaces. In this paper I will show that this statement is not correct.
The Mitsch order on a semigroup.
The mixed product decompositions of partially ordered groups
The Möbius function of the consecutive pattern poset.
The model-completion of Stone algebras
The monoid of ordered partitions of a natural number.
The -propositional calculus
T. Almada and J. Vaz de Carvalho (2001) stated the problem to investigate if these Łukasiewicz algebras are algebras of some logic system. In this article an affirmative answer is given and the -propositional calculus, denoted by , is introduced in terms of the binary connectives (implication), (standard implication), (conjunction), (disjunction) and the unary ones (negation) and , (generalized Moisil operators). It is proved that belongs to the class of standard systems of implicative...
The new interval topology on lattice products
The niche graphs of interval orders
The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if and only if...
The Nikodym property and local properties of Boolean algebras
We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.
The nil radical of an Archimedean partially ordered ring with positive squares
Let be an Archimedean partially ordered ring in which the square of every element is positive, and the set of all nilpotent elements of . It is shown that is the unique nil radical of , and that is locally nilpotent and even nilpotent with exponent at most when is 2-torsion-free. is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator. The results are applied on partially ordered rings in which every element is expressed as with positive ,...
The nonexistence of free complete vector lattices
The nonreduced order spectrum of a commutative ring.
The number of countable isomorphism types of complete extensions of the theory of Boolean algebras
There is a conjecture of Vaught [17] which states: Without The Generalized Continuum Hypothesis one can prove the existence of a complete theory with exactly nonisomorphic, denumerable models. In this paper we show that there is no such theory in the class of complete extensions of the theory of Boolean algebras. More precisely, any complete extension of the theory of Boolean algebras has either 1 or nonisomorphic, countable models. Thus we answer this conjecture in the negative for any complete...
The one-block property in varieties of semigroups.
The order dimension of Bruhat order on infinite Coxeter groups.