Ein zerlegungssatz für P(ϰ)

Abstract

We shall prove the following partition theorems:

• (1) For every setS and for each cardinal ϰ ≥ ω, |S| ≥ ϰ there exists a partitionT: [S]^ϰ → 2^ϰ such that for every pairwise disjoint familie

  

  and everyα < 2^ϰ there exists a set

  

• (2) Suppose ϰ ≥ ω, 2^<ϰ andS an arbitrary set, 2^|S| ≤ (2^ϰ)^+ω Then there exists a partitionT: P(S) → 2^ϰ such that for every pairwise disjoint family

  

  and everyα < 2^ϰ there exists a set

  

  Both theorems will give partial answers to an Erdős problem.