Homogeneous sets from several ultrafilters |
| |
Authors: | Andreas Blass |
| |
Institution: | aMathematics Department, University of Michigan, Ann Arbor, MI 48109-1043, USA |
| |
Abstract: | We consider Ramsey-style partition theorems in which homogeneity is asserted not for subsets of a single infinite homogeneous set but for subsets whose elements are chosen, in a specified pattern, from several sets in prescribed ultrafilters. We completely characterize the sequences of ultrafilters satisfying such partition theorems. (Non-isomorphic selective ultrafilters always work, but, depending on the specified pattern, weaker hypotheses on the ultrafilters may suffice.) We also obtain similar results for analytic partitions of the infinite sets of natural numbers. Finally, we show that the two P-points obtained by applying the maximum and minimum functions to a union ultrafilter are never nearly coherent. |
| |
Keywords: | Ultrafilter Selective P-point Near-coherence Partition theorem Union ultrafilter |
本文献已被 ScienceDirect 等数据库收录! |
|