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  1. Bounded arithmetic and truth definition.Gaisi Takeuti - 1988 - Annals of Pure and Applied Logic 39 (1):75-104.
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  • (1 other version)S 3 i andV 2 i (BD).Gaisi Takeuti - 1990 - Archive for Mathematical Logic 29 (3):149-169.
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  • (1 other version)S 3 i andV 2 i.Gaisi Takeuti - 1990 - Archive for Mathematical Logic 29 (3):149-169.
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  • Exponentiation and second-order bounded arithmetic.Jan Krajíček - 1990 - Annals of Pure and Applied Logic 48 (3):261-276.
    V i 2 ⊢A iff for some term t :S i 2 ⊢ “2 i exists→ A”, a bounded first-order formula, i ≥1. V i 2 is not Π b 1 -conservative over S i 2 . Any model of V 2 not satisfying Exp satisfies the collection scheme BΣ 0 1 . V 1 3 is not Π b 1 -conservative over S 2.
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  • Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
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