منابع مشابه
On Milliken-Taylor Ultrafilters
We show that there may be a Milliken-Taylor ultrafilter with infinitely many near coherence classes of ultrafilters in its projection to ω, answering a question by López-Abad. We show that k-coloured Milliken-Taylor ultrafilters have at least k + 1 near coherence classes of ultrafilters in its projection to ω. We show that the Mathias forcing with a Milliken-Taylor ultrafilter destroys all Mill...
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Milliken-Taylor systems are some of the most general infinitary configurations that are known to be partition regular. These are sets of the form MT (〈ai〉i=1, 〈xn〉n=1) = { ∑m i=1 ai ∑ t∈Fi xt : F1, F2, . . . , Fm are increasing finite nonempty subsets of N}, where a1, a2, . . . , am ∈ Z with am > 0 and 〈xn〉n=1 is a sequence in N. That is, if p(y1, y2, . . . , ym) = ∑m i=1 aiyi is a given linear...
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We obtain lower bounds for the consistency strength of fully nonregular ultrafilters on ω2.
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For a discrete group G and a discrete G-space X, we identify the Stone-Čech compactifications βG and βX with the sets of all ultrafilters on G and X, and apply the natural action of βG on βX to characterize large, thick, thin, sparse and scattered subsets of X. We use G-invariant partitions and colorings to define G-selective and G-Ramsey ultrafilters on X. We show that, in contrast to the set-...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2011
ISSN: 0029-4527
DOI: 10.1215/00294527-1499345