On the subsemilattices of first-order definable and openly first-order definable congruences of the congruence lattice of a universal algebra.
On the system of all maximal chains (antichains) of a graph.
On the tolerance extension property
On unique factorization semilattices
The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations...
On valuation in semilattices
On -operators in an arbitrary semigroup
One-variable equationally compact distributive lattices
Open problems posed at the eighth international conference on fuzzy set theory and applications
Several open problems posed during FSTA 2006 (Liptovský Ján, Slovakia) are presented. These problems concern the classification of strict triangular norms, Lipschitz t-norms, interval semigroups, copulas, semicopulas and quasi- copulas, fuzzy implications, means, fuzzy relations, MV-algebras and effect algebras.
Opérades cellulaires et espaces de lacets itérés
L’espace des configurations de points distincts de admet une filtration naturelle qui est induite par les inclusions des dans . Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des -opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.
Operations on cyclically ordered sets
Operators on C(ω^α) which do not preserve C(ω^α)
It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from onto itself such that if Y is a subspace of which is isomorphic to , then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from onto itself there is a subspace of which is isomorphic to on which the operator is an isomorphism.
Optimal decision trees on simplicial complexes.
Order complex of ideals in a commutative ring with identity
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when...
Order Preserving or Increasing Mappings Freedom or Incomparability Preserving Mappings
Ordered sets which support inverse semigroups : Three examples.
Ordered structures and projections.
Ordering the set of antichains of an ordered set.
Orderings of monomial ideals
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute bounds on the maximal order type.
Orders with ten elements are circle order.
Ordinal Bounds for Well Ordered Extensions of the Coordinatewise Partial Ordering