Small measurable cardinals
Abstract
-decomposable system. This provides us with a better lifting of elementary embeddings to symmetric extensions. In particular, this allows us to more easily lift weakly compact embeddings and thus preserve the notion of weakly critical cardinals. We use this improved lifting criterion to show that the first measurable cardinal can be the first weakly critical cardinal or the first Mahlo cardinal, both relative to the existence of a single measurable cardinal. However, if the first inaccessible cardinal is the first measurable cardinal, then in a suitable inner model it has Mitchell order of at least 2.
Fields of Study & Subjects
Advanced Topology and Set Theory
Homotopy and Cohomology in Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- Archive for Mathematical Logic
- Publisher
- Springer Science and Business Media LLC
- Volume
- 65
- Issue
- 4
- Pages
- 465–475
- Publication date
- 28 February 2026
- Language
- EN