There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
type: Item
instance of: scholarly article
title: There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
zbMATH Open document ID: 0634.03047
DOI: 10.1016/0168-0072(87)90082-0
author: Andreas Blass
author: S. Shelah
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
review text: The consistency relative to ZFC of the following mutually contradictory statements is proven. (A) Every two non-principal ultrafilters on \(\omega\) have a common image under some finite-to-one function. (B) Simple \(P_{\aleph_ 1}\)-points and simple \(P_{\aleph_ 2}\)-points both exist. The consistency of (A) is established by an iterated forcing construction that makes up the bulk of the paper. Interestingly this same construction can be modified to show (B).
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 4031670
zbMATH Keywords: P-point
zbMATH Keywords: consistency
zbMATH Keywords: ZFC
zbMATH Keywords: non-principal ultrafilters
zbMATH Keywords: iterated forcing
reviewed by: J. M. Plotkin
MaRDI profile type: Publication
full work available at URL: 0168-0072(87)90082-0
OpenAlex ID: W2144799232
Wikidata QID: Q59410903
cites work: A Characterization and Sum Decomposition for Operator Ideals
cites work: Q3906757
cites work: Special ultrafilters and cofinal subsets of \(({}^\omega \omega, <^*)\)
cites work: Composants and βN
cites work: Proper forcing
cites work: Q3708010
cites work: Families of sets and functions
cites work: Q5186348
DBLP publication ID: journals/apal/BlassS87
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description: scientific article; zbMATH DE number 4031670