A note on the Σ1collection scheme and fragments of bounded arithmetic
Zofia Adamowicz, Leszek Aleksander Kołodziejczyk · Mathematical logic quarterly · 2010
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)