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Fragments of bounded arithmetic and the lengths of proofs

✍ Scribed by Pudlák, Pavel

Book ID
124069220
Publisher
Association for Symbolic Logic
Year
2008
Tongue
English
Weight
182 KB
Volume
73
Category
Article
ISSN
0022-4812

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A note on the Σ1 collection scheme and f
A note on the Σ1 collection scheme and fragments of bounded arithmetic
✍ Zofia Adamowicz; Leszek Aleksander Kołodziejczyk 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 115 KB

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