论文标题
凝聚力原理的保护定理
Conservation theorems for the Cohesiveness Principle
论文作者
论文摘要
我们证明，在$ rca_0 +iς^0_n $上保守的凝聚力原理（COH）为$π^1_1 $，而$ rca_0 +bς^0_n $超过了所有$ n \ geq 2 $ y recursion理论手段。我们首先将COH超过$ rca_0 +bς^0_2 $表征为弱König的引理（WKL）的“跳跃”版本，并开发了合适的机械，包括Friedberg跳跃变革定理的版本。当我们将它们与有关WKL的已知结果结合在一起时，将获得主定理。在附录中，我们通过超高基础定理的$π^1_1 $保守性$π^1_1 $保守性，并提供了最新的托斯纳（Towsner）近距离跳动定理的新证明。
We prove that the Cohesiveness Principle (COH) is $Π^1_1$ conservative over $RCA_0 + IΣ^0_n$ and over $RCA_0 + BΣ^0_n$ for all $n \geq 2$ by recursion-theoretic means. We first characterize COH over $RCA_0 + BΣ^0_2$ as a `jumped' version of Weak König's Lemma (WKL) and develop suitable machinery including a version of the Friedberg jump-inversion theorem. The main theorem is obtained when we combine these with known results about WKL. In an appendix we give a proof of the $Π^1_1$ conservativity of WKL over $RCA_0$ by way of the Superlow Basis Theorem and a new proof of a recent jump-inversion theorem of Towsner.
