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Proof Theory

Gaisi Takeuti
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The article was published on 1975-01-01 and is currently open access. It has received 770 citations till now. The article focuses on the topics: Proof theory & Gentzen's consistency proof.

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Set recursion and Πhalf-logic

Jean-Yves Girard, +1 more
- 01 May 1985 - 
TL;DR: On construit par induction sur des dilateurs une hierarchie Φ F de fonctions ensemble recursives relatives a hΦ F (x)=I(F, x, h) and on demontre que si g est ensemble recursive dans h, alors g(x)≤ΦF (x) pour un certain dilateur F et pour tout x∈O n.
Journal Article

Monotone Proofs of the Pigeon Hole Principle

Albert Atserias, +2 more
- 01 Jan 2000 - 
TL;DR: A size-depth trade-oo upper bound for monotone proofs of the standard encoding of the PHP as a monot one sequent is proved, and Resolution, Cutting Planes with polynomially bounded coeecients, and Bounded-Depth Frege are exponentially separated from the monotOne Gentzen Calculus.
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On the compressibility of finite languages and formal proofs

Sebastian Eberhard, +1 more
- 05 Sep 2017 - 
TL;DR: The minimal number of productions needed for a grammar to cover a finite language L as the grammatical complexity of L is considered and it is shown that it is closely connected to well-known measures for the complexity of formal proofs in first-order predicate logic.
Journal ArticleDOI

Improved bounds on the weak Pigeonhole principle and infinitely many primes from weaker axioms

Albert Atserias
TL;DR: A size-depth trade-off upper bound is given: there are proofs of size nO(d(log(n))2/d) and depth O(d), which implies a proof of the unboundedness of primes in Iδ0 with a provably weaker 'large number assumption' than previously needed.
Journal ArticleDOI

Assignment of ordinals to patterns of resemblance

Gunnar Wilken
- 01 Jun 2007 - 
TL;DR: This paper establishes an effective order isomorphism between the classical and the new system of ordinal notations using the results from [6] and [7] and develops mutual (relatively) elementary recursive assignments which are uniform with respect to the underlying relativization.