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})+ω 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 language | Undefined/Unknown |
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Pages (from-to) | 21-40 |
Number of pages | 20 |
Journal | Periodica Mathematica Hungarica |
Volume | 15 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1 1984 |
Keywords
- AMS (MOS) subject classifications (1980): Primary 03E05, 04A20
- Combinatorial set theory
- partition calculus