منابع مشابه
Infinite dimensional perfect set theorems
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,...
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The theory of perfect graphs relates the concept of graph colorings to the concept of cliques. In this paper, we introduce the concept of a perfect graph as well as a number of graph classes that are always perfect. We next introduce both theWeak Perfect Graph Theorem and the Strong Perfect Graph Theorem and provide a proof of the Weak Perfect Graph Theorem. We also demonstrate an application o...
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TWO theorems nre proved on perfect codes. The first cne states tk.at Lloyd's theorem is true without tne assumption that the number of symbols in the alphabet is a prime power. The second thevrem asser?s the impossibility of perfect group codes over non-prime-pcwer-alphabets. IA V be a finite set, I VI = q > 2, and let 1 <_ e 2 ye be Ia:ional integers. We pu?iV= (1, 2,. .. . n). Forv=(Vi)~=l E ...
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(Received September 1, 2009) Abstract. For a nontrivial connected graph G, let c : V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v ∈ V (G), the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6= NC(v) for every pair u, v of adjacent vertices of G. The minimum number of c...
متن کاملRectangular Axioms, Perfect Set Properties and Decomposition
We consider three combinatorial topics appearing in Gödel’s manuscript Some considerations leading to the probable conclusion that the true power of the continuum is א2. These statements concern rectangular functions, perfect set properties, and covering properties of sets of reals. We consider these statements in light of more recent work on the set theory of the reals.
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2008
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm201-2-6