On Milliken-Taylor Ultrafilters

Notre Dame Journal of Formal Logic 52 (4):381-394 (2011)
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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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References found in this work

Near Coherence of Filters. I. Cofinal Equivalence of Models of Arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
Forcing and Stable Ordered–Union Ultrafilters.Todd Eisworth - 2002 - Journal of Symbolic Logic 67 (1):449-464.
Some Filters of Partitions.Pierre Matet - 1988 - Journal of Symbolic Logic 53 (2):540-553.

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