On the structure of generalized P-points
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 \(U(\kappa)\).
scientific article; zbMATH DE number 3875283