Between Ramsey and measurable cardinals
Abstract
We study several intertwined hierarchies between $κ$-Ramsey cardinals and measurable cardinals to illuminate the structure of the large cardinal hierarchy in this region. In particular, we study baby versions of measurability introduced by Bovykin and McKenzie and some variants by locating these notions in the large cardinal hierarchy and providing characterisations via filter games. As an application, we determine the theory of the universe up to a measurable cardinal.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- Journal of the Mathematical Society of Japan
- Publisher
- Mathematical Society of Japan (Project Euclid)
- Volume
- -1
- Issue
- -1
- Pages
- 1-48
- Publication date
- 8 April 2026
- Language
- EN