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We show that any theory of tame henselian valued fields is NIP if and only if the theory of its residue field and the theory of its value group are NIP. Moreover, we show that if (K, v) is a henselian valued field of residue characteristic char (K v) = p such that if p > 0 , depending on the characteristic of K either the degree of imperfection or the index of the pth powers is finite, then (K, v) is NIP iff Kv is NIP and v is roughly separably tame. [ABSTRACT FROM AUTHOR]

We study definable types in the theory of closed ordered differential fields (CODF). We show a condition for a type to be definable, then we prove that definable types are dense in the Stone space of CODF. [ABSTRACT FROM AUTHOR]

The computable dimension of a structure counts the number of computable copies up to computable isomorphism. In this paper, we consider the possible computable dimensions for various classes of computable ordered fields. We show that computable ordered fields with finite transcendence degree are computably stable, and thus have computable dimension 1. We then build computable ordered fields of infinite transcendence degree which have infinite computable dimension, but also such fields which are computably categorical. Finally, we show that 1 is the only possible finite computable dimension for any computable archimedean field. [ABSTRACT FROM AUTHOR]

Pour tout entier n, on construit des sous-groupes, infiniment définissables de rang de Lascar ω, du groupe additif d'un corps séparablement clos. [ABSTRACT FROM AUTHOR]