Submission date: 12 October 2014.

Abstract:

[To appear in the Journal of Symbolic Logic]
Let M be a C-minimal structure and T its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than ∞ ordered by inclusion). We present a description of definable locally constant functions f:M\rightarrow T in C-minimal structures having a canonical tree with infinitely many branches at each node and densely ordered branches. This provides both a description of definable subsets of T in one variable and analogues of known results in algebraically closed valued fields.

Mathematics Subject Classification: 12L12, 12J10, 03C64

Keywords and phrases:

Full text arXiv 1410.3144: pdf, ps.