论文标题
$ VTC^0 $的型号为指数整数零件
Models of $VTC^0$ as exponential integer parts
论文作者
论文摘要
我们证明，有限的算术理论的非标准模型$ \ mathsf {vtc^0} $的非标准模型的（加法）有序的组还原，并以一种丰富的语言递归饱和，谓词表达整数，理性和对数有界数的数字。结合我们先前关于构建实际指数函数的结果，在$ \ mathsf {vtc^0} $的模型的完成中，我们表明，$ \ Mathsf {vtc^0} $的每一个可计数模型都是实用指数字段的指数级数。
We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory $\mathsf{VTC^0}$ are recursively saturated in a rich language with predicates expressing the integers, rationals, and logarithmically bounded numbers. Combined with our previous results on the construction of the real exponential function on completions of models of $\mathsf{VTC^0}$, we show that every countable model of $\mathsf{VTC^0}$ is an exponential integer part of a real-closed exponential field.
