Submission date: 11 January 2013.

Abstract:

There are several equivalent characterizations of the valuation rank of an ordered field (endowed with its natural valuation). In this paper, we extend the theory to the case of an ordered difference field and introduce the notion of difference rank. We characterize the difference rank as the quotient modulo the equivalence relation naturally induced by the automorphism (which encodes its growth rate). In analogy to the theory of convex valuations, we prove that any linearly ordered set can be realized as the difference rank of an ordered difference field.

Mathematics Subject Classification: Primary 03C60, 06A05, 12J15: Secondary 12L12, 26A12

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Full text arXiv 1301.2611: pdf, ps.