论文标题
什么是反向数学中有效的递归递归？
What is effective transfinite recursion in reverse mathematics?
论文作者
论文摘要
在反向数学的背景下，有效的转递递归是指我们可以沿任意井订单构建递归序列序列的原理，前提是每个集合都是$δ^0_1 $ - 可定义的相对于recursion的先前阶段。众所周知，该原理在$ \ mathbf {aca} _0 $中可证明。在本说明中，我们认为有效的递归的共同表述过于限制。然后，我们提出了一个更加自由的配方，该公式看起来很自然，并且仍然可以在$ \ mathbf {aca} _0 $中证明。
In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is $Δ^0_1$-definable relative to the previous stages of the recursion. It is known that this principle is provable in $\mathbf{ACA}_0$. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and is still provable in $\mathbf{ACA}_0$.
