We study variants of Buss’s theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on \(\hat{\varPi }^{b}_i\) induction schemes, which were so far neglected in the literature. We present inclusions and conservation results between the systems (including a witnessing theorem for \(T^i_2\) and \(S^i_2\) of a new form), results on numbers of instances of the axioms or rules, connections to reflection principles for quantified propositional calculi, and separations between the systems.

中文翻译：

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有界算术中的归纳规则

我们研究了通过归纳方案不允许参数使用以及紧密相关的归纳推理规则的有界算术公有制理论的Buss理论的变体。我们特别强调\（\ hat {\ varPi} ^ {b} _i \） 归纳方案，该归纳方案到目前为止在文献中都被忽略。我们给出系统之间的包含和守恒结果（包括新形式的\（T ^ i_2 \）和 \（S ^ i_2 \）的见证定理），关于公理或规则实例数量的结果，与反射的联系定量命题计算的原理，以及系统之间的分离。