无参数理解并不意味着二阶Peano算法中的完全理解
The parameterfree Comprehension does not imply the full Comprehension in the 2nd order Peano arithmetic
摘要：
考虑了二阶Peano算法$\text{PA}_2$的无参数部分$\text{PA}_2^\ast$。我们使用一个产品/迭代Sacks强制定义一个$ω$模型的$\text{PA}_2^\ast + \text{CA}(Σ^1_2)$，其中一个例子的完整的理解模式$\text{CA}$失败。使用科恩的强迫，我们还定义了一个$ω$模型的$\text{PA}_2^\ast$，其中不是每一个集有它的补充，因此，完整的$\text{CA}$失败，而基本的方式。
英文摘要：
The parameter-free part $\text{PA}_2^\ast$ of $\text{PA}_2$, the 2nd order Peano arithmetic, is considered. We make use of a product/iterated Sacks forcing to define an $ω$-model of $\text{PA}_2^\ast + \text{CA}(Σ^1_2)$, in which an example of the full Comprehension schema $\text{CA}$ fails. Using Cohen's forcing, we also define an $ω$-model of $\text{PA}_2^\ast$, in which not every set has its complement, and hence the full $\text{CA}$ fails in a rather elementary way.
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