Computing maximal chains
نویسندگان
چکیده
منابع مشابه
Computing maximal chains
In [Wol67], Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note that all chains in a wpo are well-ordered.) We prove that such maximal chain cannot be found computably, not even hyperarithmetically: No hyperarithmetic set can compute maximal chains in all computable wpos. However, we prove that almost every set, in the sense of categ...
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This note is intended as a supplement and clarification to the proof of Theorem 3.3 of [1]; namely, it is consistent that b = ℵ 1 yet for every ultrafilter U on ω there is a ≤ * chain {f ξ : ξ ∈ ω 2 } such that {f ξ /U : ξ ∈ ω 2 } is cofinal in ω/U. The general outline of the the proof remains the same. In other words, a ground model is taken which satisfies 2 ℵ0 = ℵ 1 and in which there is a ♦...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2012
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-012-0289-4