We investigate definability in henselian fields. Specifically, we are interested in those sets and substructures that are existentially definable or definable with `few' parameters. Our general approach is to use various versions of henselianity to understand the `local structure' of these definable sets.
The fields in which we are most interested are those of positive characteristic, for example the local fields Fq( ... [truncated at 450 characters in length]
|Creator||William George Anscombe;|
|Key phrase||logic 03C model theory 12L field theory polynomials|
|Abstract||A suitable subcategory of aﬃne Azumaya algebras is deﬁned and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is deﬁned and a ﬁrst-order theory is associated to each object. For those theories satisfying a certain technical con ... [truncated at 450 characters in length]|
|Key phrase||03C 16G 18F 81R|