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 ∀x∃yA(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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Avigad, J.: A realizability interpretation for classical arithmetic. In Buss and Hájek and Pudlák, Logic Colloquium ‘98. Lecture Notes in Logic 13, 57–90, (2000) AK Peters
Schwichtenberg, H.: The Handbook of Mathematical Logic. Proof theory: Some aspects of cut-elimination, North-Holland, 1977 pp. 867–895
Troelstra, A.S.: Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Springer. With contributions by A.S. Troelstra, C.A. Smoryński, J.I. Zucker and W.A. Howard, 1973
Kreisel, G.: Interpretation of Analysis by means of Functionals of Finite Type. Constructivity in Mathematics. A. Heyting, North-Holland, 1959, pp. 101–128
Kreisel, G.: On Weak Completeness of Intuitionistic Predicate Logic. J. Symb. Logic. 27, 139–158 (1962)
Dragalin, A.G.: New forms of realizability and Markov’s rule (Russian). Doklady, 251, 534–537, (1980)
Friedman, H.: Higher Set Theory, Classically and Intuitionistically Provably Recursive Functions, Springer, 1978, 669, Springer Lecture Notes, 21–27
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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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DOI: https://doi.org/10.1007/s00153-004-0233-3