Article contents
$G_{\delta \sigma }$ GAMES AND INDUCTION ON REALS
Published online by Cambridge University Press: 13 September 2021
Abstract
It is shown that the determinacy of $G_{\delta \sigma }$ games of length $\omega ^2$ is equivalent to the existence of a transitive model of ${\mathsf {KP}} + {\mathsf {AD}} + \Pi _1\textrm {-MI}_{\mathbb {R}}$ containing $\mathbb {R}$ . Here, $\Pi _1\textrm {-MI}_{\mathbb {R}}$ is the axiom asserting that every monotone $\Pi _1$ operator on the real numbers has an inductive fixpoint.
- Type
- Article
- Information
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic
References
- 1
- Cited by