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Functional interpretation and inductive definitions
 Journal of Symbolic Logic
"... Abstract. Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finitetype functionals defined using transfinite recursion on wellfounded trees. 1. ..."
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Cited by 7 (2 self)
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Abstract. Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finitetype functionals defined using transfinite recursion on wellfounded trees. 1.
A realizability interpretation for classical arithmetic
 In Buss, Hájek, and Pudlák eds., Logic colloquium ’98, AK Peters, 57–90
, 2000
"... Summary. A constructive realizablity interpretation for classical arithmetic is presented, enabling one to extract witnessing terms from proofs of Σ1 sentences. The interpretation is shown to coincide with modified realizability, under a novel translation of classical logic to intuitionistic logic, ..."
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Cited by 5 (4 self)
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Summary. A constructive realizablity interpretation for classical arithmetic is presented, enabling one to extract witnessing terms from proofs of Σ1 sentences. The interpretation is shown to coincide with modified realizability, under a novel translation of classical logic to intuitionistic logic, followed by the FriedmanDragalin translation. On the other hand, a natural set of reductions for classical arithmetic is shown to be compatible with the normalization of the realizing term, implying that certain strategies for eliminating cuts and extracting a witness from the proof of a Σ1 sentence are insensitive to the order in which reductions are applied. 1
Bounded Modified Realizability
, 2005
"... We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov’s principle but meshes well w ..."
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Cited by 1 (1 self)
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We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov’s principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak König’s lemma. We discuss some applications, as well as some previous results in the literature. 1