论文标题
关于二阶均匀反射片段的注释
A note on fragments of uniform reflection in second order arithmetic
论文作者
论文摘要
我们考虑在分析层次结构中对二阶算术理论的分析层次结构中均匀反射的片段。主要结果是，对于任何二阶算术理论，$ t_0 $扩展了$ {\ sf rca} _0 $和Axiomatiziz -a $π^1_ {k+2} $句子，对于任何$ n \ geq k+1 $ \ = \ T_0+ \ Mathrm {Ti} _ {\ varpi^1_n}（\ varepsilon_0），\] \ [T_0+ \ \ \ \ \ \ \ \ \ \ \ Mathrm {rfn} _ {\ varsigma \ Mathrm {ti} _ {\ varpi^1_n}（\ varepsilon_0）^{ - }，\]，其中$ t $ as $ t $ as $ t_0 $充分吸引，$ \ mathrm {ti} _ {ti} _ {对于$ \ varpi^1_n $公式，无需$ \ VAREPSILON_0 $的转移感应不带有set参数。
We consider fragments of uniform reflection for formulas in the analytic hierarchy over theories of second order arithmetic. The main result is that for any second order arithmetic theory $T_0$ extending ${\sf RCA}_0$ and axiomatizable by a $Π^1_{k+2}$ sentence, and for any $n\geq k+1$, \[ T_0+ \mathrm{RFN}_{\varPi^1_{n+2}}(T) \ = \ T_0 + \mathrm{TI}_{\varPi^1_n}(\varepsilon_0), \] \[ T_0+ \mathrm{RFN}_{\varSigma^1_{n+1}}(T) \ = \ T_0+ \mathrm{TI}_{\varPi^1_n}(\varepsilon_0)^{-}, \] where $T$ is $T_0$ augmented with full induction, and $\mathrm{TI}_{\varPi^1_n}(\varepsilon_0)^{-}$ denotes the schema of transfinite induction up to $\varepsilon_0$ for $\varPi^1_n$ formulas without set parameters.
