[No title available]

F. Galvin, Karel L Prikry, K. Wolfsdorf

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Abstract

We shall prove the following partition theorems: (1) For every set S and for each cardinal κ{script} ≥ ω, |S| ≥ κ{script} there exists a partition T: [S]κ{script} → 2κ{script} such that for every pairwise disjoint familie[Figure not available: see fulltext.] and every α < 2κ{script} there exists a set[Figure not available: see fulltext.] (2) Suppose κ{script} ≥ ω, 2<κ{script} and S an arbitrary set, 2|S| ≤ (2κ{script}) Then there exists a partition T: P(S) → 2κ{script} such that for every pairwise disjoint family[Figure not available: see fulltext.] and every α < 2κ{script} there exists a set[Figure not available: see fulltext.] Both theorems will give partial answers to an Erdo{combining double acute accent}s problem.

Original languageUndefined/Unknown
Pages (from-to)21-40
Number of pages20
JournalPeriodica Mathematica Hungarica
Volume15
Issue number1
DOIs
StatePublished - Mar 1 1984

Keywords

  • AMS (MOS) subject classifications (1980): Primary 03E05, 04A20
  • Combinatorial set theory
  • partition calculus

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