On the structure of generalized P-points
type: Item
instance of: scholarly article
title: On the structure of generalized P-points
zbMATH Open document ID: 0549.04004
DOI: 10.1007/BF01193916
author: Rodolfo Talamo
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: For an infinite cardinal \(\kappa\), \(U(\kappa)\) is the space of uniform ultrafilters on \(\kappa\). It is known that for \(\kappa\) below the first measurable cardinal and of uncountable cofinality, \(U(\kappa)\) cannot contain P-points. In Ann. Math. II. Ser. 90, 23-32 (1969; Zbl 0187.269) \textit{S. Negrepontis} defined an appropriate notion of generalized P- points for uncountable cardinals. The author finds for every regular \(\kappa\), assuming \(2^{\kappa}=\kappa^+\), a generalized P-point which is not Rudin- Keisler minimal. As a corollary to his construction, he obtains the fact that, assuming \(2^{\kappa}=\kappa^+\), for \(\kappa >\omega\) the set of generalized P-points in \(U(\kappa)\) is not \(U(\kappa)\)-homogeneous. The paper concludes with some remarks concerning the existence of various kinds of P-points in \(U(\kappa)\).
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 3875283
zbMATH Keywords: uniform ultrafilters
zbMATH Keywords: generalized P-points
zbMATH Keywords: uncountable cardinals
reviewed by: K. P. Hart
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01193916
OpenAlex ID: W2314154456
description: scientific article; zbMATH DE number 3875283