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$G_{\delta \sigma }$ 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.
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic
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