Submission date: 4 August 2017

Abstract:

Analysability of finite U-rank types are explored both in general and in the theory DCF_0. The well-known fact that the equation δ(log δ x)=0 is analysable in but not almost internal to the constants is generalized to show that (log δ ... log δ)_n x=0 is not analysable in the constants in (n-1)-steps. The notion of a canonical analysis is introduced - namely an analysis that is of minimal length and interalgebraic with every other analysis of that length. Not every analysable type admits a canonical analysis. Using properties of reductions and coreductions in theories with the canonical base property, it is constructed, for any sequence of positive integers (n_1, ... , n_l), a type in DCF_0 that admits a canonical analysis with the property that the ith step has U-rank n_i.

Mathematics Subject Classification: 03C45 (Primary) 12H05 (Secondary)

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Full text arXiv 1708.01633: pdf, ps.