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- Title
A note on the Σ<sub>1</sub> collection scheme and fragments of bounded arithmetic.
- Authors
Adamowicz, Zofia; Kołodziejczyk, Leszek Aleksander
- Abstract
We show that for each n ≥ 1, if T2n does not prove the weak pigeonhole principle for Σbn functions, then the collection scheme B Σ1 is not finitely axiomatizable over T2n. The same result holds with Sn2 in place of T 2n (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects
ARITHMETIC; FUNCTIONS of bounded variation; AXIOMS; MATHEMATICAL formulas; MODULAR arithmetic
- Publication
Mathematical Logic Quarterly, 2010, Vol 56, Issue 2, p126
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.200810043