MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1557

Preprint Number 1557

Previous Next Preprint server


1557. Sergey Sudoplatov
Ranks for families of theories and their spectra
E-mail:

Submission date: 24 January 2019

Abstract:

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.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1901.08464: pdf, ps.


Last updated: March 23 2021 10:21 Please send your corrections to: