Let K be an algebraically closed eld of any characteristic, complete with respect to a non-trivial ultrametric absolute value. We prove a quantiier simpliication theorem which enables us to show that the class of subanalytic sets based on the Tate rings over K is closed under complementation and closure and that these sets have smooth stratiications.
In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quantifier elimination theorem for (complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quantifier elimination is… (More)
In this paper, we establish a basic dimension theory for rigid subanalytic sets, and we prove a Smooth Stratification Theorem for such sets, in all characteristics.
OBJECTIVE Eosinophil predominant inflammation characterises histological features of eosinophilic oesophagitis (EoE). Endoscopy with biopsy is currently the only method to assess oesophageal mucosal inflammation in EoE. We hypothesised that measurements of luminal eosinophil-derived proteins would correlate with oesophageal mucosal inflammation in children… (More)
Working over an algebraically closed, complete, non-Archimedean, non-trivially valued eld of characteristic zero, we show that (i) any subanalytic subset of a one-dimensional semialgebraic set is semialgebraic; (ii) any one-dimensional sub-analytic set is semianalytic; and (iii) any subanalytic subset of a two-dimensional semianalytic set is semianalytic.… (More)
The influence of sampling strategy on estimates of effective population size (N e ) from single-sample genetic methods has not been rigorously examined, though these methods are increasingly used. For headwater salmonids, spatially close kin association among age-0 individuals suggests that sampling strategy (number of individuals and location from which… (More)
In this paper, we establish a basic dimension theory for rigid subanalytic sets, and we prove a Smooth Stratiication Theorem for such sets, in all characteristics.