科研之友
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摘要
In this paper, we introduce the notion of almost decidable predicates of real variables. The notion comes from the concept of decidability of number theoretical predicates together with the idea of effective convergence in computable analysis. The weakness of traditional definitions of decidability is discussed. The definition of almost decidable predicates of real variables is given. It is proved that some commonly used predicates on R-n such as 2; and is an element of, = and subset of between computable reals and recursive open/closed sets are almost decidable, which justifies our definition of decidability in Euclidean spaces. Additionally, the relation between almost decidability and computability of reals and recursiveness of subsets of R-n is considered, which provides a bridge to include our works here to the earlier literature on computability in analysis.
- 出版日期2005-8
- 单位中山大学
