论文标题
在有序组的半横向扩展中
On semibounded expansions of ordered groups
论文作者
论文摘要
我们探讨了任意有序组的“半决赛”扩展；也就是说，没有定义整个宇宙领域的扩展。我们表明，如果$ \ MATHCAL r = \ langle r，<， +，\ dots \ rangle $是半曲调的O-Minimal结构，$ p \ subseteq r $ A集满满足某些可驯服条件，那么$ \ \ \ langle \ cal r，p \ cal r，p \ rangle $仍然是半oc的。示例包括当$ \ Mathcal {r} = \ langle \ mathbb r，<，+，（x \mapStoλx）_ {λ\ in \ mathbb r}，\ cdot_ {[0，1]^2} \ rangle $，和$ p = 2^^is AN at AN AN AN AN AN AN时，作为一个应用程序，我们获得了在这种$ \ langle \ Mathcal r，p \ rangle $中可以定义的平滑功能，在$ \ Mathcal r $中是可以定义的。
We explore "semibounded" expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $\mathcal R=\langle R, <, +, \dots\rangle$ is a semibounded o-minimal structure and $P\subseteq R$ a set satisfying certain tameness conditions, then $\langle \cal R, P\rangle$ remains semibounded. Examples include the cases when $\mathcal{R}=\langle \mathbb R,<,+, (x\mapsto λx)_{λ\in \mathbb R}, \cdot_{ [0, 1]^2} \rangle$, and $P= 2^\mathbb Z$ or $P$ is an iteration sequence. As an application, we obtain that smooth functions definable in such $\langle \mathcal R, P\rangle$ are definable in $\mathcal R$.
