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We obtain lower bounds for the consistency strength of fully nonregular ultrafilters on ω 2. ... We build on their argument to obtain lower consistency bounds for fully nonregular ultrafilters on ω 2 : Theorem 1. Suppose there is a fully nonregular ultrafilter U on ω 2 . ... proved that if there is a nonregular ultrafilter on ω 1 , then 0 exists. ...doi:10.2178/jsl/1309952522 fatcat:ikzqp5fqfffhjm2cqtal5drxfu
Handbook of the History of Logic
Silver's own account of the discovery of his famous theorem is as follows: The immediate stimulus for this result was some work of Kanamori and Magidor 1 concerning nonregular ultrafilters on ω 1 . ... the bound (ℵ ω1 ) ℵ1 < ℵ ω2 from Chang's conjecture. ...doi:10.1016/b978-0-444-51621-3.50007-4 fatcat:fr3pdoy3nbdn5pc4pz52reng24
The problems have been updated with current information on solutions with bibliographic references. ... Are there weak P ω2 -points in U (ω 1 ), the space of uniform ultrafilters on ω 1 ? Solution. Yes. J. Baker and K. ... Rudin) In ZFC, are there two free ultrafilters on ω with no common finite-to-one image? Under MA there are such ultrafilters. S2. (van Douwen and Solution. ...arXiv:math/0312456v1 fatcat:g5aorxz3z5btlbxoawere25mdy