Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topolo...

We have proved in an earlier paper that the complexity of the list homomorphism problem, to a fixed graph H , does not change when the input graphs are restricted to have bounded degrees (except in the trivial case when the bound is two). By way of contrast, we show in this paper that the extension problem, again to a fixed graph H , can, in some cases, become easier for graphs with bounded deg...

A class of structures is said to have the homomorphism-preservation property just in case every firstorder formula that is preserved by homomorphisms on this class is equivalent to an existential-positive formula. It is known by a result of Rossman that the class of finite structures has this property and by previous work of Atserias et al. that various of its subclasses do. We extend the latte...

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs [1] showed that any Z-module homomorphism of ...

Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. This paper focuses on the intermediate class S∧ of (unital) meet semilattices. Any S ∈ S∧ embeds into the algebraic closure system Filt(Filt(S)). This iterated filter completion, denoted Filt(S), is a compact and ∨∧ -dense exte...

A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the infinite line Z. It is shown that if the maximal degree of G is ‘sub-logarithmic’, then the range of such a homomorphism is super-constant. Furthermore, some exam...

We consider the entailment problem in the fragment of first-order logic (FOL) composed of existentially closed conjunctions of literals (without functions), denoted FOL(∃,∧,¬a). This problem can be recast as several fundamental problems in artificial intelligence and databases, namely query containment for conjunctive queries with negation, clause entailment for clauses without functions and qu...