# The theory of classical valuations

@inproceedings{Ribenboim1999TheTO, title={The theory of classical valuations}, author={Paulo Ribenboim}, year={1999} }

1 Absolute Values of Fields.- 1.1. First Examples.- 1.2. Generalities About Absolute Values of a Field.- 1.3. Absolute Values of Q.- 1.4. The Independence of Absolute Values.- 1.5. The Topology of Valued Fields.- 1.6. Archimedean Absolute Values.- 1.7. Topological Characterizations of Valued Fields.- 2 Valuations of a Field.- 2.1. Generalities About Valuations of a Field.- 2.2. Complete Valued Fields and Qp.- 3 Polynomials and Henselian Valued Fields.- 3.1. Polynomials over Valued Fields.- 3.2…

## 108 Citations

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This paper uses model theory to exhibit a uniform method, on various theories of valued fields, for deriving an algebraic characterization of functions over a valued field which are integral definite on some definable set.

### Model Theory of Valued fields

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These notes focus mainly on the model theory of algebraically closed valued fields (loosely referred to as ACVF). This subject begins with work by A. Robinson in the 1950s (see the proof of model…

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### Simple valuation ideals of order 3 in two-dimensional regular local rings

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Let (R, m) be a 2-dimensional regular local ring with alge- braically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is…