In this paper, for a henselian valued field (K, v) of arbitrary rank and an extension w of v to K(X), we use abstract key polynomials for w to obtain distinguished pairs and saturated distinguished chains.

In this paper, for a henselian valued field (K, v) of arbitrary rank and an extension w of v to K(X), we use abstract key polynomials for w to give a connection between complete sets, saturated distinguished chains and Okutsu frames. Further, for a valued field (K, v), we also obtain a close connection between complete set of ABKPs for w and Maclane-Vaquié chains of w.

In this paper, for a valued field (K, v) of arbitrary rank and an extension w of v to K(X), a relation between complete sequence of abstract key polynomials, Maclane-Vaquié chain and pseudo-convergent sequence of transcendental type is given.

In this paper, for a valued field [Formula: see text] of arbitrary rank and an extension [Formula: see text] of [Formula: see text] to [Formula: see text] a relation between induced complete sequences of abstract key polynomials and MacLane-Vaquié chains is given.

In this paper, for a henselian valued field [Formula: see text] of arbitrary rank and an extension [Formula: see text] of [Formula: see text] to [Formula: see text] we use abstract key polynomials for [Formula: see text] to obtain distinguished pairs and saturated distinguished chains.