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TRUTH AND FEASIBLE REDUCIBILITY
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- Journal:
- The Journal of Symbolic Logic / Volume 85 / Issue 1 / March 2020
- Published online by Cambridge University Press:
- 20 September 2019, pp. 367-421
- Print publication:
- March 2020
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- Article
- Export citation
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Let
${\cal T}$ be any of the three canonical truth theories CT− (compositional truth without extra induction), FS− (Friedman–Sheard truth without extra induction), or KF− (Kripke–Feferman truth without extra induction), where the base theory of 
${\cal T}$ is PA (Peano arithmetic). We establish the following theorem, which implies that 
${\cal T}$ has no more than polynomial speed-up over PA.Theorem.
${\cal T}$is feasibly reducible to PA, in the sense that there is a polynomial time computable function f such that for every
${\cal T}$-proof π of an arithmetical sentence ϕ, f (π) is a PA-proof of ϕ.
