论文标题
关于序数及其反向的可计算嵌入的注释
A Note on Computable Embeddings for Ordinals and Their Reverses
论文作者
论文摘要
我们继续研究成对结构的可计算嵌入，即含有精确的两个非同构结构的类。令人惊讶的是，即使对于一些简单的线性顺序，可计算的嵌入也会引起非平凡的度结构。我们的主要结果表明，尽管$ \ {ω\ cdot 2，ω^\ star \ cdot 2 \} $可计算嵌入在$ \ {ω^2，{（ω^2）}^\ star \} $中可在$ \ {ω^2，{（ω^2）}^\ star \} $中嵌入$ \ {ω^2中，对于任何天然数字$ k \ geq 3 $。
We continue the study of computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree structure. Our main result shows that although $\{ω\cdot 2, ω^\star \cdot 2\}$ is computably embeddable in $\{ω^2, {(ω^2)}^\star\}$, the class $\{ω\cdot k,ω^\star \cdot k\}$ is \emph{not} computably embeddable in $\{ω^2, {(ω^2)}^\star\}$ for any natural number $k \geq 3$.
