论文标题
关于有序字段的可计算性
On the computability of ordered fields
论文作者
论文摘要
在本文中，我们开发了由总计可计算功能（递归功能）产生的可计算实数类别的一般技术，并对基本操作进行了特殊限制，以便研究以下问题：生成类别是否是一个真正的封闭字段，以及是否存在可计算的生成类的计算呈现。我们证明了一系列定理，这些定理导致结果是，即使对于$ e_n $ compotable的实数，也没有可计算时间的可计算演示文稿，其中$ e_n $是grzegorczyk hierArchy，$ n \ geq 2 $。我们还提出了Archimedean有序场的可计算前置性标准。
In this paper we develop general techniques for classes of computable real numbers generated by subsets of total computable (recursive functions) with special restrictions on basic operations in order to investigate the following problems: whether a generated class is a real closed field and whether there exists a computable presentation of a generated class. We prove a series of theorems that lead to the result that there are no computable presentations neither for polynomial time computable no even for $E_n$-computable real numbers, where $E_n$ is a level in Grzegorczyk hierarchy, $n \geq 2$. We also propose a criterion of computable presentability of an archimedean ordered field.
