论文标题
$ t $ -Convex有价值的领域具有钢化
$T$-convex valued fields with tempered exponentiation
论文作者
论文摘要
我们继续努力，努力将功率结合的$ t $ convex有价值的领域的结构（通常称为TCVF）的理论。在本文中，我们的重点是一定的扩展，该扩展配备了估值环以外的速度指数函数。为了构建这种调整的指数函数，签名的值组也被转换为$ t $ Plus指示的模型，实际上是通过对角横截面和角度组件图的组成（一个部分）残留场的（部分）确定的。从某种意义上说，由此产生的通用理论TKVF是功率结合的TCVF和指数TCVF之间的中间点。这个理论是相当良好的。特别是，我们表明它以自然语言，维度的概念，广义的Euler特征等，接受量化剂的消除。
We continue the effort of grokking the structure of power-bounded $T$-convex valued fields, whose theory is in general referred to as TCVF. In the present paper our focus is on certain expansion of it that is equipped with a tempered exponential function beyond the valuation ring. In order to construct such a tempered exponential function, the signed value group is also converted into a model of $T$ plus exponentiation and is in fact identified with (a section of) the residue field via the composition of a diagonal cross-section and an angular component map. In a sense, the resulting universal theory TKVF is a halfway point between power-bounded TCVF and exponential TCVF. This theory is reasonably well-behaved. In particular, we show that it admits quantifier elimination in a natural language, a notion of dimension, a generalized Euler characteristic, etc.
