On Milliken-Taylor Ultrafilters
Heike Mildenberger
Source: Notre Dame J. Formal Logic Volume 52, Number 4
(2011), 381-394.
Abstract
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-colored 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 Milliken-Taylor ultrafilters from the ground model.
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Keywords: Milliken-Taylor ultrafilters; P-points; near coherence classes of ultrafilters; forcing; preserving ultrafilters
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Notre Dame Journal of Formal Logic
