Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...

Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty co...

What largeness and structural assumptions on A ⊆ [R]ω can guarantee the existence of a non-empty perfect set P ⊆ R such that [P ]ω ⊆ A? Such a set P is called A-homogeneous. We show that even if A is open, in general it is independent of ZFC whether for a cardinal κ, the existence of an A-homogeneous set H ∈ [R]κ implies the existence of a non-empty perfect A-homogeneous set. On the other hand,...

Let I be a non empty set, let X be a non-empty many sorted set indexed by I, and let i be an element of I. Note that X(i) is non empty. In the sequel S will be a non void non empty many sorted signature and V will be a non-empty many sorted set indexed by the carrier of S. Let us consider S, V . The functor S -Terms(V ) yielding a non empty subset of FinTrees(the carrier of DTConMSA(V )) is def...

On December 2, when Venezuelans delivered President Hugo Chávez his first electoral defeat in nine years, most analysts were taken by surprise. According to o⁄cial results, 50.7 percent of voters rejected Chávez’s proposed constitutional reform, which would have expanded executive power, gotten rid of presidential term limits, and paved the way for the construction of a “socialist” economy. It ...