Placing text on a collection of curves in a bounded region
β Scribed by V. V. Brovarnik
- Publisher
- Springer US
- Year
- 1991
- Tongue
- English
- Weight
- 637 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1573-8337
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract By suitably adapting an argument of Hirschfeld (see [2, Chapter 9]), we show that there is a single Ξ~1~ formula that defeats βbounded collectionβ for any model of II~2~ Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MS
Bounded arithmetic, collection principle, weak pigeonhole principle. ## MSC (2000) 03F30 We show that for each n β₯ 1, if T n 2 does not prove the weak pigeonhole principle for Ξ£ b n functions, then the collection scheme BΞ£1 is not finitely axiomatizable over T n 2 . The same result holds with S n