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Axiomatizations and Conservation Results for Fragments of Bounded Arithmetic
, 1990
"... This paper presents new results on axiomatizations for fragments of Bounded Arithmetic which improve upon the author's dissertation. It is shown that (# i+1 )PIND and strong # i replacement are consequences of S 2 . Also # i+1 IND is a consequence of T 2 . The latter result is prove ..."
Abstract

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This paper presents new results on axiomatizations for fragments of Bounded Arithmetic which improve upon the author's dissertation. It is shown that (# i+1 )PIND and strong # i replacement are consequences of S 2 . Also # i+1 IND is a consequence of T 2 . The latter result is proved by showing that S i+1 conservative over 2 . Furthermore, S i+1 replacement with respect to Boolean combinations of # i+1 formulas. 1