Modified Bar Recursion and Classical Dependent Choice
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منابع مشابه
Parametrised bar recursion: A unifying framework for realizability interpretations of classical dependent choice
During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with some form of bar recursion, which realizes the negative translation of either countable or countable dependent choice. In this work we present the many varia...
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We introduce a variant of Spector’s bar recursion (called “modified bar recursion”) in finite types to give a realizability interpretation of the classical axiom of countable choice allowing for the extraction of witnesses from proofs of Σ1 formulas in classical analysis. As a second application of modified bar recursion we present a bar recursive definition of the fan functional. Moreover, we ...
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