Bounded arithmetic, collection principle, weak pigeonhole principle. ## MSC (2000) 03F30 We show that for each n ≥ 1, if T n 2 does not prove the weak pigeonhole principle for Σ b n functions, then the collection scheme BΣ1 is not finitely axiomatizable over T n 2 . The same result holds with S n
✦ LIBER ✦
A note on the Σ1 spectrum of a theory
✍ Scribed by Michael Möllerfeld; Michael Rathjen
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 51 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0933-5846
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