On the elimination of imaginaries from certain valued fields

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

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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DOI 10.1016/0168-0072(93)90222-y
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References found in this work BETA

Descriptive Set Theory.Yiannis N. Moschovakis - 1981 - Journal of Symbolic Logic 46 (4):874-876.
Une Théorie de Galois Imaginaire.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (4):1151-1170.
Some Applications of the Notions of Forcing and Generic Sets.[author unknown] - 1972 - Journal of Symbolic Logic 37 (3):612-613.
On Definable Subsets of P-Adic Fields.Angus MacIntyre - 1976 - Journal of Symbolic Logic 41 (3):605-610.

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Citations of this work BETA

More on Imaginaries in P-Adic Fields.Philip Scowcroft - 1997 - Journal of Symbolic Logic 62 (1):1-13.

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