Stable domination and independence in algebraically closed valued fields
| dc.creator | Haskell, Deirdre | |
| dc.creator | Hrushovski, Ehud | |
| dc.creator | Macpherson, Dugald | |
| dc.date | 2005-11-11 | |
| dc.date | 2006-11-20 | |
| dc.date.accessioned | 2026-07-07T06:51:09Z | |
| dc.date.available | 2026-07-07T06:51:09Z | |
| dc.description | We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of stably dominated types, showing they enjoy an excellent independence theory, as well as a theory of definable types and germs of definable functions. In Part B, we show that the general theory applies to ACVF. Over a sufficiently rich base, we show that every type is stably dominated over its image in the value group. For invariant types over any base, stable domination coincides with a natural notion of `orthogonality to the value group'. We also investigate other notions of independence, and show that they all agree, and are well-behaved, for stably dominated types. One of these is used to show that every type extends to an invariant type; definable types are dense. Much of this work requires the use of imaginary elements. We also show existence of prime models over reasonable bases, possibly including imaginaries. | |
| dc.identifier | https://arxiv.org/abs/math/0511310 | |
| dc.identifier | http://arxiv.org/abs/math/0511310 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104894 | |
| dc.subject | Logic | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 12J10, 03C45, 03C60 | |
| dc.title | Stable domination and independence in algebraically closed valued fields | |
| dc.type | text |