Applied Proof Theory - Proof Interpretations and their Use in Mathematics

@inproceedings{Kohlenbach2008AppliedPT,
  title={Applied Proof Theory - Proof Interpretations and their Use in Mathematics},
  author={Ulrich Kohlenbach},
  booktitle={Springer Monographs in Mathematics},
  year={2008}
}
Corrected version Nov.20: a confused slide on the functional interpretation of weak compactness as well as a slide stating a bound on Browder's theorem have been deleted as the latter has been superseded meanwhile: weak compactess can be bypassed resulting in a primitive recursive bound. 
Highly Influential
This paper has highly influenced 20 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Topics from this paper.
146 Citations
8 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 146 extracted citations

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Conjecture: no uniformity w.r.t. C Baillon/Bruck (1996): Uniformity w.r.t. x0, f , C for λ k Full uniformity for general λ k

  • Goebel, Kirk
  • Conjecture: no uniformity w.r.t. C Baillon/Bruck…
  • 1990

Uniformity w.r.t. x0 ∈ C (λ k := λ) Uniformity for unif

  • O Edelstein, Brien
  • Uniformity w.r.t. x0 ∈ C (λ k := λ) Uniformity…
  • 1978

X unif. convex, general λ k , X , no uniformity Ishikawa

  • Groetsch
  • 1972

X unif.convex,λ k = λ, no uniformity

  • Browder, Petryshyn
  • X unif.convex,λ k = λ, no uniformity
  • 1967

For a (·) : equivalent to adding a bound b on the metric d as input

  • For a (·) : equivalent to adding a bound b on the…

Further applications of proof theory to mathematics Numerous further applications in metric fixed point theory Convex Analysis (1), Abstr

  • Briseid, Gerhardy, Lambov, K Leustean
  • Fixed Point Theory (1), Proc. Fixed Point Theory

New results on Hilbert's 17th problem (Delzell, Inventiones Math. etc.) Proof theory and Ramsey's theorem for pairs: see the talk be A. Kreuzer at this meeting

  • New results on Hilbert's 17th problem (Delzell…

] : can treat statements involving an ε-net. If only the proof uses such a net: still much easier to formalize

  • T [ X Benefits, C Tot
  • ] : can treat statements involving an ε-net. If…

Similar Papers

Loading similar papers…