论文标题
算术模型的结构复杂性
The structural complexity of models of arithmetic
论文作者
论文摘要
我们计算了Peano算术的可数模型的Scott等级。我们表明，没有非标准模型可以使Scott排名小于$ω$，而真正的算术的非标准模型必须使Scott的排名大于$ω$。除此之外，没有限制。通过$δ^{\ mathrm {in}} _ {1} $ bi-bi-interprotability减少，从线性订购等级到规范结构$ω$ - 任意完成$ t $ t $ $ \ \\ mathrm {pa} $的$ t $ t $ t $ t $ t $的模型，我们显示的每一个可计数$ $ $ a $ a $ nistable $ a $ act的模型concott carcott concott carcott of carcon concott of a concott of a concott of a concott of a concott。
We calculate the possible Scott ranks of countable models of Peano arithmetic. We show that no non-standard model can have Scott rank less than $ω$ and that non-standard models of true arithmetic must have Scott rank greater than $ω$. Other than that there are no restrictions. By giving a reduction via $Δ^{\mathrm{in}}_{1}$ bi-interpretability from the class of linear orderings to the canonical structural $ω$-jump of models of an arbitrary completion $T$ of $\mathrm{PA}$ we show that every countable ordinal $α>ω$ is realized as the Scott rank of a model of $T$.
