A Theorem on Shortening the Length of Proof in Formal Systems of Arithmetic
✍ Scribed by Robert A. Di Paola
- Book ID
- 124972417
- Publisher
- Association for Symbolic Logic
- Year
- 1975
- Tongue
- English
- Weight
- 168 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0022-4812
- DOI
- 10.2307/2272163
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📜 SIMILAR VOLUMES
## Abstract Let ℸ be the set of Gödel numbers Gn(__f__) of function symbols __f__ such that PRA ⊢ and let γ be the function such that We prove: (1) The r. e. set ℸ is m‐complete; (2) the function γ is not primitive recursive in any class of functions {__f__~1~, __f__~2~, ⃛} so long as each __f~i~
A particularly well suited induction hypothesis is employed to give a short and relatively direct formulation of van der Waerden's argument which establishes that for any partition of the natural numbers into two classes, one of the classes contains arbitrarily long arithmetic progressions.