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We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over system T to Spector’s bar recursion, whereas the other is T-equivalent to modified bar recursion. Modified bar recursion itself is shown to arise directly from the iteration of a different binary product of ‘skewed’ selection functions. Iterations of the dependent binary products are also considered but in all cases are shown to be T-equivalent to the iteration of the simple products.



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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
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