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A Note on Conservativity Relations among Bounded Arithmetic Theories

✍ Scribed by Russell Impagliazzo; Jan Krajíček

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
98 KB
Volume
48
Category
Article
ISSN
0044-3050

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A note on the Σ1 collection scheme and f
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✍ 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