Uniform Procedures in uncountable Structures.
JOURNAL OF SYMBOLIC LOGIC(2018)
摘要
This article contributes to the general program of extending techniques and ideas of effective algebra to computable metric space theory. It is well-known that relative computable categoricity (to be defined) of a computable algebraic structure is equivalent to having a c.e. Scott family with finitely many parameters (e.g., [ID. The first main result of the article extends this characterisation to computable Polish metric spaces. The second main result illustrates that just a slight change of the definitions will give us a new notion of categoricity unseen in the countable case (to be stated formally). The second result also shows that the characterisation of computably categorical closed subspaces of R(n )contained in [17] cannot be improved. The third main result extends the characterisation to not necessarily separable structures of cardinality kappa using kappa-computability.
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关键词
relative computable categoricity,effective Polish spaces,admissible recursion theory
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