منابع مشابه
Forcing Positive Partition Relations
We show how to force two strong positive partition relations on u, and use them in considering several well-known open problems. In [32] Sierpiñski proved that the well-known Ramsey Theorem [27] does not generalize to the first uncountable cardinal by constructing a partition [ío,]2 = KQ U Kx with no uncountable homogeneous sets. Sierpinski's partition has been analyzed in several directions. O...
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متن کاملSpecial Rumen Microbiology
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متن کاملForcing Many Positive Polarized Partition Relations Between A Cardinal and Its Powerset
A fairly quotable special, but still representative, case of our main result is that for 2 ≤ n < ω, there is a natural numberm(n) such that, the following holds. Assume GCH: If λ < μ are regular, there is a cofinality preserving forcing extension in which 2 = μ and, for all σ < λ ≤ κ < η such that η(+m(n)−1) ≤ μ, ((η)σ)→ ((κ)σ) (1)n η . This generalizes results of [3], Section 1, and the forcin...
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ژورنال
عنوان ژورنال: Science
سال: 2002
ISSN: 0036-8075,1095-9203
DOI: 10.1126/science.296.5577.2299a