On interpretability in set theories I, Comm. Math. Univ. Carolinae, 12, pp. 73--79. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Logic of Provability - Japaridze, de Jongh (1998) (13 citations) (Correct)
....part of the fixed point theorem fails for R. Simpler proofs for the completeness theorems were given in de Jongh [1987] and Voorbraak [1988] There are connections between this work in provability logic and speed up. First, de Jongh and Montagna [1988,1989] gave a new simpler proof of Parikh [1971] s theorem that, for any provably recursive function g there is a sentence ff provable in PA such that PA proves PrPA (p ff q) by a much shorter proof in the sense of g (a g b iff g(a) b) than it proves A itself. In de Jongh and Montagna [1988] this was done for g the identity function by ....
....then proves that as soon as is a theorem of T , is true in M , and the clause (a) of the lemma expresses just this fact; as for clause (b) it is an immediate consequence of (a) for PA Compl ff : Pr ff (p q) Pr ff (p: q) and PA t: t . 12.7. Theorem. Orey [1961] H ajek [1971,1972]) PA : For superarithmetic theories T and S the following are equivalent: i) T is interpretable in S , ii) for all m, S Con T#m , iii) T is Pi 1 conservative over S . Proof. i) ii) Suppose t = h ; oei is an interpretation of T in S . Let be the conjunction of all axioms of T ....
On interpretability in set theories I, Comm. Math. Univ. Carolinae, 12, pp. 73--79.
The Logic of Provability - Japaridze, de Jongh (1997) (13 citations) (Correct)
....part of the fixed point theorem fails for R. Simpler proofs for the completeness theorems were given in de Jongh [1987] and Voorbraak [1988] There are connections between this work in provability logic and speed up. First, de Jongh and Montagna [1988,1989] gave a new simpler proof of Parikh [1971] s theorem that, for any provably recursive function g there is a sentence ff provable in PA such that PA proves PrPA (p ff q) by a much shorter proof in the sense of g (a g b iff g(a) b) than it proves A itself. In de Jongh and Montagna [1988] this was done for g the identity function by ....
....then proves that as soon as is a theorem of T , is true in M , and the clause (a) of the lemma expresses just this fact; as for clause (b) it is an immediate consequence of (a) for PA Compl ff : Pr ff (p q) Pr ff (p: q) and PA t: t . 12.7. Theorem. Orey [1961] H ajek [1971,1972]) PA : For superarithmetic theories T and S the following are equivalent: i) T is interpretable in S , ii) for all m, S Con T#m , iii) T is Pi 1 conservative over S . Proof. i) ii) Suppose t = h ; oei is an interpretation of T in S . Let be the conjunction of all axioms of T ....
On interpretability in set theories I, Comm. Math. Univ. Carolinae, 12, pp. 73--79.
Chapter Vii - The Logic Of (1968) (1 citation) (Correct)
No context found.
On interpretability in set theories I, Comm. Math. Univ. Carolinae, 12, pp. 73--79.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC