论文标题
无参数理解并不意味着第二阶的全部理解Peano算术
The parameterfree Comprehension does not imply the full Comprehension in the 2nd order Peano arithmetic
论文作者
论文摘要
考虑到$ \ text {pa} _2 _2 _2 $，第二阶Peano arithmetic的$ \ text {pa} _2 $ ast $ ast $ ast $ ast $ ast $。我们利用产品/迭代的麻袋强迫定义了$ \ text {pa} _2^\ ast + ast + \ ast + \ text {ca}（σ^1_2）$的$ω$ -MODEL，其中一个完整的理解模式$ \ textma $ \ text {ca} $失败。使用Cohen的强迫，我们还定义了$ \ text {pa} _2^\ ast $的$ω$ -MODEL，其中并非每个集合都有其补充，因此以相当基本的方式失败了。
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.
