Modified Bar Recursion

Forfattere

  • Ulrich Berger
  • Paulo B. Oliva

DOI:

https://doi.org/10.7146/brics.v9i14.21732

Resumé

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 Sigma_1 formulas in classical analysis. As a second application of modified bar recursion we present a bar recursive definition of the fan functional. Moreover, we show that modified bar recursion exists in M (the model of strongly majorizable functionals) and is not S1-S9 computable in C (the model of total functionals). Finally, we show that modified bar recursion defines Spector's bar recursion primitive recursively.

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Publiceret

2002-04-05

Citation/Eksport

Berger, U., & Oliva, P. B. (2002). Modified Bar Recursion. BRICS Report Series, 9(14). https://doi.org/10.7146/brics.v9i14.21732

Nummer

Nr. 14 (2002): RS-14 Modified Bar Recursion

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