We consider two kinds of reducibilities on finite families of predicates on a countable set: the definability of predicates and their complements of one family via another by means of existential formulas with parameters and the same definability on isomorphism types of families. Ordered structures of degrees generated by families of unary predicates are described. It is proved that for both reducibilities, there exist continuum many minimal nonzero degrees.

中文翻译：

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Δ-可定义性的最小谓词

我们考虑可数集合上谓词的有限族的两种可约性：通过带参数的存在公式和对同构类型的族的相同可定义性，谓词及其对一个族的补语的可定义性。描述了由一元谓词族生成的度数的有序结构。证明了对于这两种可约性，都存在许多最小非零度的连续统。