关于有界算术中归纳模式的注记
A Note on Induction Schemas in Bounded Arithmetic
摘要：
众所周知，巴斯的有界算术$S^{1}_{2}$理论证明了$Σ_{0}^{b}(Σ_{1}^{b})-LIND$ ;然而，我们证明了艾伦的$D_{2}^{1}$不证明$Σ_{0}^{b}(Σ_{1}^{b})-LLIND$，除非$P = NC$。我们也给出了$S^{1}_{2}$的一些有趣的替代公理化。
英文摘要：
As is well known, Buss' theory of bounded arithmetic $S^{1}_{2}$ proves $Σ_{0}^{b}(Σ_{1}^{b})-LIND$; however, we show that Allen's $D_{2}^{1}$ does not prove $Σ_{0}^{b}(Σ_{1}^{b})-LLIND$ unless $P = NC$. We also give some interesting alternative axiomatisations of $S^{1}_{2}$.
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