Stationary reflection using ancestrally forced conditions
arXiv:2607.28350
summary
The paper introduces a new forcing method that produces models where stationary sets reflect at the successor of a singular cardinal, using a κ⁺‑supercompact cardinal to achieve countable simultaneous reflection at ℵ_{ω₁+1}.
Abstract
We introduce a new method for obtaining models of stationary reflection at the successor of a singular cardinal of any cofinality. In particular, starting from a cardinal which is -supercompact, we get a model of countable simultaneous reflection at .
Topics & keywords
#set theory#large cardinals#stationary reflection#singular cardinals#forcingstationary reflectionsupercompact cardinalforcing techniquesingular cardinalsimultaneous reflection