Proof interpretations: what they are and what they are good for
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1 s: what they are and what they are good for Jaime Gaspar INRIA Paris-Rocquencourt, πr 2, Univ Paris Diderot, Sorbonne Paris Cité, F Le Chesnay, France Financially supported by the French Fondation Sciences Mathématiques de Paris
2 I: S 1 S 2 such that
3 I: S 1 S 2 such that Geometry Talks about points, lines, planes,... Consistency T is consistent Has axioms like twocl distinct consistent points determine a line
4 I: S 1 S 2 such that Arithmetic Consistency T is consistent Talks about 0,1,2,... CL isand consistent +, Has axioms like x +y = y +x
5 I: S 1 S 2 such that
6 I: S 1 S 2 such that ǫ>0 m n m x n <ǫ f ǫ>0 n f(ǫ) x n <ǫ
7 I: S 1 S 2 such that
8 I: S 1 S 2 such that T 1 = CL T 2 = IL I = negative translation
9 I: S 1 S 2 such that IL proves S program IL proves S 1 (S 1 S 2) S 2 x,f f(x)
10 I: S 1 S 2 such that
11 I: S 1 S 2 such that T 1 = ZF + S infinite S S S T 2 = ZF +AC I = classical realisability
12 I: S 1 S 2 such that
13 I: S 1 S 2 such that T 1 ZF = PA doesn t ω + n pprime n<p 2n T 2 prove = T 1 AC I = monotone functional after a negative translation
14 I: S 1 S 2 such that
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