理论族及其谱的秩
Ranks for families of theories and their spectra
摘要：
我们定义了理论族的秩和度，类似于Morley秩和度，以及Cantor-Bendixson秩和度，以及完全超越理论族的概念。找到了$e$ -谱关于秩和度的界，证明了在$E$ -闭包下秩和度是保持不变的，并刻画了秩和度的值.证明了可数语言的$E$ -闭包和$e$ -谱值的基数意义下的完全超越族的判别准则。
英文摘要：
We define ranks and degrees for families of theories, similar to Morley rank and degree, as well as Cantor-Bendixson rank and degree, and the notion of totally transcendental family of theories. Bounds for $e$-spectra with respect to ranks and degrees are found. It is shown that the ranks and the degrees are preserved under $E$-closures and values for the ranks and the degrees are characterized. Criteria for totally transcendental families in terms of cardinality of $E$-closure and of the $e$-spectrum value, for a countable language, are proved.
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