Metric invariants over Henselian valued fields

In this paper we generalize the notion of a saturated distinguished sequence associated to a separable element , over a local field K [J. Number Theory 79 (1999) 217; J. Number Theory 52 (1995) 98] to the case of an arbitrary Henselian field (K,v). We use these distinguished sequences to study various arithmetic and metric invariants of a, generalizing some results from [J. Math. Kyoto Univ. 30 (1990) 207; J. Number Theory 79 (1999) 217; A. Popescu, N. Popescu, M. Vâjâitu, A. Zacharescu, Chains of metric invariants over p-adic fields, Acta Arith., to appear; J. Number Theory 52 (1995) 98; Portugal. Math. 54 (1997) 73]. In the process we also obtain some Ax–Sen type inequalities (see [J. Algebra 15 (1970) 417; Ann. of Math. 90 (1969) 33]).