期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2010
卷号：24
页码：56-66
DOI：10.4204/EPTCS.24.10
出版社：Open Publishing Association
摘要：We examine the relation of BSS-reducibility on subsets of the real numbers. The question was asked recently (and anonymously) whether it is possible for the halting problem H in BSS-computation to be BSS-reducible to a countable set. Intuitively, it seems that a countable set ought not to contain enough information to decide membership in a reasonably complex (uncountable) set such as H. We confirm this intuition, and prove a more general theorem linking the cardinality of the oracle set to the cardinality, in a local sense, of the set which it computes. We also mention other recent results on BSS-computation and algebraic real numbers.
