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.

© 1996-9

1999-05-26