A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.

We investigate several variants of the homomorphism problem: given two relational structures, is there a homomorphism from one to the other? The input structures are possibly infinite, but definable by first-order interpretations in a fixed structure. Their signatures can be either finite or infinite but definable. The homomorphisms can be either arbitrary, or definable with parameters, or defi...

the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.

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...

The relation of existence of a homomorphism on the class of all relational structures of a fixed type is reflexive and transitive; it is a quasiorder. There are standard ways to transform a quasiorder into a partial order – by identifying equivalent objects, or by choosing a particular representative for each equivalence class. The resulting partial order is identical in both cases. Properties ...

Solution: For the action mentioned in the hint, the stabilizer of the coset eH (e is the identity) is H since gH = H implies that g ∈ H. The kernel K of the homomorphism of G into the permutation group of the cosets is a normal subgroup of G which is the intersection of stabilizers of all cosets. In particular the kernel K of the above homomorphism is a subgroup of H. Its index in G is equal to...

1. Abstract characterization of Dn The group Dn has two generators r and s with orders n and 2 such that srs−1 = r−1. We will show any group with a pair of generators like r and s (except for their order) admits a homomorphism onto it from Dn, and is isomorphic to Dn if it has the same size as Dn. Theorem 1.1. Let G be generated by elements a and b where an = 1 for some n ≥ 3, b2 = 1, and bab−1...

ρ(e)(x) = e · x A1 = x = 1X(x) for all g, h ∈ G and x ∈ X. Thus ρ(gh) = ρ(g) ◦ ρ(h), ρ(e) = 1X and ρ is hence a homomorphism of monoids G → M(X). Then we note 1X = ρ(e) = ρ(gg ) = ρ(g) ◦ ρ(g) and similarly 1X = ρ(g) ◦ ρ(g) and so the ρ(g) are bijections G → G for all g ∈ G. Thus ρ is a homomorphism G → Σ(X). Given a homomorphism λ : G → Σ(X), in order for it to be the action homomorphism of an ...

We study the image of a transfer homomorphism in the stable homotopy groups of spheres. Actually, we show that an element of order 8 in the 18 dimensional stable stem is in the image of a double transfer homomorphism, which reproves a result due to P J Eccles that the element is represented by a framed hypersurface. Also, we determine the image of the transfer homomorphism in the 16 dimensional...