On the elimination of imaginaries from certain valued fields

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Annals of Pure and Applied Logic 61 (3):241-276 (1993)
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Abstract

A nontrivial ring with unit eliminates imaginaries just in case its complete theory has the following property: every definable m-ary equivalence relation E may be defined by a formula f = f, where f is an m-ary definable function. We show that for certain natural expansions of the field of p-adic numbers, elimination of imaginaries fails or is independent of ZPC. Similar results hold for certain fields of formal power series

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10.1016/0168-0072(93)90222-y

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Citations of this work

More on imaginaries in p-adic fields.Philip Scowcroft - 1997 - Journal of Symbolic Logic 62 (1):1-13.

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References found in this work

On definable subsets of p-adic fields.Angus MacIntyre - 1976 - Journal of Symbolic Logic 41 (3):605-610.
Une théorie de galois imaginaire.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (4):1151-1170.
Algebraic theories with definable Skolem functions.Lou van den Dries - 1984 - Journal of Symbolic Logic 49 (2):625-629.
Undecidable-Rings.Raphael M. Robinson - 1952 - Journal of Symbolic Logic 17 (4):268-269.

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