A Computational Interpretation of the Axiom of Determinacy in Arithmetic

We investigate the computational content of the axiom of determinacy (AD) in the setting of classical arithmetic in all finite types with the principle of dependent choices (DC). By employing the notion of realizability interpretation for arithmetic given by Berardi, Bezem and Coquand (1998), we interpret the negative translation of AD. Consequently, the combination of the negative translation with this realizability semantics can be seen as a model of DC, AD and the negation of the axiom of choice at higher types. In order to understand the computational content of AD, we explain, employing Coquand\u27s game theoretical semantics, how our realizer behaves

Arguing Using Opponent Models

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