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$G_{\delta \sigma }$
GAMES AND INDUCTION ON REALS
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 86 / Issue 4 / December 2021
- Published online by Cambridge University Press:
- 13 September 2021, pp. 1676-1690
- Print publication:
- December 2021
-
- Article
- Export citation
-
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.
