Definable functions and stratifications in power-bounded \(T\)-convex fields. (English) Zbl 1458.14063
T-stratification for henselian valued fields of equi-characteristic zero is defined, and a sufficient condition for valued fields admitting t-stratification is provided in [I. Halupczok, Proc. London Math. Soc. 109, 1304–1362 (2014; Zbl 1382.03061)]. This paper demonstrates that \(T\)-convex fields given in [L. van den Dries et al., J. Symbolic Logic 60, 74–102 (1995; Zbl 0856.03028)] satisfy the sufficient condition when \(T\) is a power-bounded complete o-minimal theory extending the theory of real closed fields. It also demonstrates that \(T\)-convex field does not admit t-stratification when the exponentiation is definable.
Reviewer: Fujita Masato (Kure)
MSC:
| 14P10 | Semialgebraic sets and related spaces |
| 03C98 | Applications of model theory |
| 03C64 | Model theory of ordered structures; o-minimality |
Keywords:
real closed valued fields; \(o\)-minimality; \(T\)-convex fields; \(t\)-stratifications; Jacobian property; \(b\)-minimality; Whitney stratificationsReferences:
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