Abstract
AbstractAnalysability of finiteU-rank types are explored both in general and in the theory${\rm{DC}}{{\rm{F}}_0}$. The well-known fact that the equation$\delta \left( {{\rm{log}}\,\delta x} \right) = 0$is analysable in but not almost internal to the constants is generalized to show that$\underbrace {{\rm{log}}\,\delta \cdots {\rm{log}}\,\delta }_nx = 0$is not analysable in the constants in$\left( {n - 1} \right)$-steps. The notion of acanonical analysisis 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$\left( {{n_1}, \ldots ,{n_\ell }} \right)$, a type in${\rm{DC}}{{\rm{F}}_0}$that admits a canonical analysis with the property that theith step hasU-rank${n_i}$.
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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1. Internality of logarithmic-differential pullbacks;Transactions of the American Mathematical Society;2020-04-16