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Showing 1 to 7 of 7 for “"valued fields"”.
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Definable equivalence relations and disc spaces of algebraically closed valued fields
… of ($\rm I\!N, +, \cdot$), algebraically closed fields, and real closed fields. (Note: theories here are first-order, with equality, and to be consistent with other formulations of EI, we require at least two distinct constants to be definable.)
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Model Theory of Valued Difference Fields
… we investigate the model theoretic properties of valued difference fields, that is, valued fields equipped with a distinguished automorphism. We carry out this study in two different contexts depending on the interaction between the valuation and the distinguished automorphism. In both contexts we …
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Valued Difference Fields as Modules Over Twisted Polynomial Rings
More generally, the thesis considers arbitrary valued fields instead of (k((t)), v), with the Frobenius map replaced by an arbitrary self-embedding of the valued field. Many results go through in this more general setting with some additional assumptions.
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Derivations on o-minimal fields
… our attention to $T$-convex $T$-differential fields. These are models $K\models T$ equipped with a $T$-derivation which is continuous with respect to a $T$-convex valuation ring of $K$, as defined by van den Dries and Lewenberg. We show that if $K$ is a $T$-convex $T$-differential field, then …
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Truncation in differential Hahn fields
… truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra …
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The Pila-Wilkie theorem and analytic Ax-Kochen-Ersov theory
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Algebraically closed fields with characters; differential-henselian monotone valued differential fields
… theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and angular component map.