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Preprint Number 1557

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1557. Sergey Sudoplatov
Ranks for families of theories and their spectra

Submission date: 24 January 2019


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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Full text arXiv 1901.08464: pdf, ps.

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