منابع مشابه
Rectangular 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.
متن کاملPerfect-Set Properties in L(R)[U]
It is well-known that various forms of the axiom of choice lead to sets of reals with singular properties. One of the most familiar examples is Bernstein's totally imperfect set of reals obtained using a well-ordering of R, i.e., a set of reals X which is neither disjoint nor includes a nonempty perfect set of reals (see [Be]). That some form of AC is needed to get such a set was proved much la...
متن کاملInfinite 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,...
متن کاملSet Colorings in Perfect Graphs
(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 کاملSome properties of n-capable and n-perfect groups
In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1998
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1752