在常数中可分析的微分闭域中构造类型
Constructing Types in Differentially Closed Fields that are Analysable in the Constants
摘要：
有限$U$秩类型的可分析性在一般情况下和理论$\mathrm{DCF}_0$中进行了探讨。将方程$δ(\mathrm{log}δx)=0$在常数中可分析但几乎不在常数内部这一众所周知的事实推广到$\underbrace{\mathrm{log}δ...\mathrm{log}δ}_n x=0$在$(n-1)$ -步中的常数中不可分析。引入了\emph{canonical analysis}的概念--即一个最小长度的分析和与该长度的所有其他分析的代数间分析。不是每一个可分析类型都允许进行规范分析。利用规范基性质理论中约简和余约简的性质，对任意正整数序列$(n_1,...,n_\ell)$，构造了一个$\mathrm{DCF}_0$中的类型，该类型允许规范分析，其性质是$i$第n步具有$U$ -秩$n_i$ .
英文摘要：
Analysability of finite $U$-rank types are explored both in general and in the theory $\mathrm{DCF}_0$. The well-known fact that the equation $δ(\mathrm{log}δx)=0$ is analysable in but not almost internal to the constants is generalized to show that $\underbrace{\mathrm{log}δ...\mathrm{log}δ}_n x=0$ is not analysable in the constants in $(n-1)$-steps. The notion of a \emph{canonical analysis} is introduced -- namely an analysis that is of minimal length and interalgebraic with every other analysis of that length. Not every analysable type admits a canonical analysis. Using properties of reductions and coreductions in theories with the canonical base property, it is constructed, for any sequence of positive integers $(n_1,...,n_\ell)$, a type in $\mathrm{DCF}_0$ that admits a canonical analysis with the property that the $i$th step has $U$-rank $n_i$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
