On the index sets of Σ-subsets of the real numbers

A. S. Morozov

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On the index sets of Σ-subsets of the real numbers

机译：关于实数Σ子集的索引集

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摘要

We compute the levels of complexity in analytical and arithmetical hierarchies for the sets of the Σ-formulas defining in the hereditarily finite superstructure over the ordered field of the reals the classes of open, closed, clopen, nowhere dense, dense subsets of ? n , first category subsets in ? n as well as the sets of pairs of Σ-formulas corresponding to the relations of set equality and inclusion which are defined by them. It is also shown that the complexity of the set of the Σ-formulas defining connected sets is at least Π11.

机译：我们计算在解析和算术层次结构中，对于在有序域的遗传上有限的超结构中定义的Σ-公式集的集合，其开，闭，扇形，无处稠密的？ n，第一类子集在哪里？ n以及与它们定义的集合相等和包含关系对应的成对的Σ公式对。还表明，定义连通集的Σ-式的集合的复杂度至少为Π11。

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来源
《Siberian Mathematical Journal》 |2008年第6期|共7页
作者
A. S. Morozov;
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正文语种 eng
中图分类数学;
关键词
computability over the reals; sigma-formula; admissible set; index set; hereditarily finite superstructure;

机译：实数可计算性;sigma公式;可允许集;索引集;遗传有限的上层结构;

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On the index sets of Σ-subsets of the real numbers

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