## Kreisel Conjecture

A Conjecture in Decidability theory which postulates that, if there is a uniform bound to the lengths of shortest proofs of instances of , then the universal generalization is necessarily provable in Peano Arithmetic. The Conjecture was proven true by M. Baaz in 1988 (Baaz and Pudlák 1993).

References

Baaz, M. and Pudlák P. ``Kreisel's Conjecture for . In Arithmetic, Proof Theory, and Computational Complexity, Papers from the Conference Held in Prague, July 2-5, 1991 (Ed. P. Clote and J. Krajicek). New York: Oxford University Press, pp. 30-60, 1993.

Dawson, J. ``The Gödel Incompleteness Theorem from a Length of Proof Perspective.'' Amer. Math. Monthly 86, 740-747, 1979.

Kreisel, G. ``On the Interpretation of Nonfinitistic Proofs, II.'' J. Symbolic Logic 17, 43-58, 1952.