Notre Dame Journal of Formal Logic

On Milliken-Taylor Ultrafilters

Heike Mildenberger

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 52, Number 4 (2011), 381-394.

Dates
First available in Project Euclid: 4 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1320427643

Digital Object Identifier
doi:10.1215/00294527-1499345

Mathematical Reviews number (MathSciNet)
MR2855877

Zentralblatt MATH identifier
1258.03056

Subjects
Primary: 03E05: Other combinatorial set theory 03E17: Cardinal characteristics of the continuum 03E35: Consistency and independence results

Keywords
Milliken-Taylor ultrafilters P-points near coherence classes of ultrafilters forcing preserving ultrafilters

Citation

Mildenberger, Heike. On Milliken-Taylor Ultrafilters. Notre Dame J. Formal Logic 52 (2011), no. 4, 381--394. doi:10.1215/00294527-1499345. https://projecteuclid.org/euclid.ndjfl/1320427643


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