The Undecidability of k-Provability (1989)
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by
Samuel R. Buss
| Venue: | Annals of Pure and Applied Logic |
| Citations: | 25 - 0 self |
BibTeX
@ARTICLE{Buss89theundecidability,
author = {Samuel R. Buss},
title = {The Undecidability of k-Provability},
journal = {Annals of Pure and Applied Logic},
year = {1989},
volume = {53}
}
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Abstract
The k-provability problem is, given a first order formula φ and an integer k, to determine if φ has a proof consisting of k or fewer lines (i.e., formulas or sequents). This paper shows that the k-provability problem for the sequent calculus is undecidable. Indeed, for every r.e. srt X...
Citations
| 124 | The undecidability of the second-order unification problem - Goldfarb - 1981 |
| 96 | Proof Theory - Takeuti - 1987 |
| 23 | Some results on the length of proofs - Parikh - 1973 |
| 20 | P.: The number of proof lines and the size of proofs in first order logic - Krajíček, Pudlák - 1988 |
| 10 | A unification-theoretic method for investigating the k-provability problem - Farmer - 1991 |
| 8 | Implicit proofs - Kraj'icek - 1987 |
| 7 | A uni algorithm for second order monadic terms - Farmer - 1988 |
| 7 | Sets of theorems with short proofs - Richardson - 1974 |
| 6 | Proof theory: some personal recollections - Kreisel - 1987 |
| 6 | Reconstruction of the proof from its scheme - Orevkov - 1984 |
| 4 | On the length of proofs in a formal system of recursive arithmetic - Miyatake - 1980 |
| 4 | On the lengths of proofs in formal systems - Miyatake - 1980 |
| 4 | A note on a formalized arithmetic with function symbols and - Yukami - 1978 |
| 1 | Generalizations of proofs - Krajcek - 1987 |
