A simple -point and a simple -point
Christian Bräuninger
Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, GermanyHeike Mildenberger
Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany
![A simple $P_{\aleph_1}$-point and a simple $P_{\aleph_2}$-point cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-25-issue-12.png&w=3840&q=90)
Abstract
We answer the long-standing question whether it is consistent to have simple -points of two different characters. For a filter over Guzmán and Kalajdzievski introduced a parametrised version of Miller forcing called . By combining iterands of the type with others we establish: It is consistent relative to ZFC that there is a simple -point and a simple -point. A main technical point is the use of properness and descriptive complexity in the limit steps of uncountable cofinality.
Cite this article
Christian Bräuninger, Heike Mildenberger, A simple -point and a simple -point. J. Eur. Math. Soc. 25 (2023), no. 12, pp. 4971–4996
DOI 10.4171/JEMS/1299