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A realizability interpretation for classical analysis

Abstract.

We present a realizability interpretation for classical analysis–an association of a term to every proof so that the terms assigned to existential formulas represent witnesses to the truth of that formula. For classical proofs of Π2 sentences ∀xyA(x,y), this provides a recursive type 1 function which computes the function given by f(x)=y iff y is the least number such that A(x,y).

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Author information

Correspondence to Henry Towsner.

Additional information

Mathematics Subject Classification (2000): 03F35,03F05

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Towsner, H. A realizability interpretation for classical analysis. Arch. Math. Logic 43, 891–900 (2004). https://doi.org/10.1007/s00153-004-0233-3

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Keywords

  • Classical Analysis
  • Realizability Interpretation
  • Classical Proof
  • Existential Formula
  • Recursive Type