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Preprint Number 1552
1552. Sylvy Anscombe, Philip Dittmann, and Arno Fehm Approximation theorems for spaces of localities E-mail: Submission date: 9 January 2019 Abstract: The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations exist, for example for finitely many (Krull) valuations, where one usually requires that these are independent, i.e. induce different topologies on the field. Ribenboim proved a generalization for finitely many valuations where the condition of independence is relaxed for a natural compatibility condition, and Ershov proved a statement about simultaneously approximating finitely many different elements with respect to finitely many possibly infinite sets of pairwise independent valuations. We prove approximation theorems for infinite sets of valuations and orderings without requiring pairwise independence. Mathematics Subject Classification: 12J10, 12J15, 13A18, 13F30, 12E30 Keywords and phrases: |

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