In this paper we investigate the consistency and consequences of the downward Löwenheim–Skolem–Tarski theorem for extension of the first order logic by the Magidor–Malitz quantifier. We derive some combinatorial results and improve the known upper bound for the consistency of Chang’s conjecture at successor of singular cardinals.
Bibliographical notePublisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.
- Chang’s conjecture
- Large cardinals
- Magidor–Malitz quantifiers