Abstract

It is well-known that every c.e. Turing degree is the degree of categoricity of a rigid structure. In this work we study the possibility of extension of this result to properly 2-c.e. degrees. We found a condition such that if a \(\Delta^{0}_{2}\)-degree is a degree of categoricity of a rigid structure and satisfies this condition then it must be c.e. Also we show that degrees of non-categoricity are dense in the c.e. degrees.

中文翻译：

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强烈的分类度和弱密度

摘要

众所周知，每个图灵度都是刚性结构的分类度。在这项工作中，我们研究了将该结果扩展到适当的2 ce度的可能性。我们发现了一个条件，如果\（\ Delta ^ {0} _ {2} \）- degree是刚性结构的分类度，并且满足该条件，那么它必须是ce。类别在ce级别密集。