__Research article:__

** Samuel R. Buss.
"Axiomatizations and conservation results for fragments of bounded
arithmetic."
In **

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** Abstract: **This paper presents new results on
axiomatizations for fragments of Bounded Arithmetic which improve upon the author's
dissertation. It is shown that $(\Sigma_{i+1}^b \cap \Pi_{i+1}^b)$-PIND and strong
$\Sigma_i^b$-replacement are consequences of $S_2^i$. Also $\Delta_{i+1}^b$-IND is a
consequence of $T_2^i$. The latter result is proved by showing that $S_2^{i+1}$ is
$\forall\exists\Sigma_{i+1}^b$-conservative over $T_2^i$. Furthermore, $S_2^{i+1}$ is
conservative over $T_2^i + \Sigma_{i+1}^b\mbox{-replacement}$ with respect to Boolean
combinations of $\Sigma_{i+1}^b$-formulas.