کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661793 | 1633469 | 2013 | 11 صفحه PDF | دانلود رایگان |
We give a definition, in the ring language, of ZpZp inside QpQp and of Fp[[t]]Fp[[t]] inside Fp((t))Fp((t)), which works uniformly for all p and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining ZpZp inside QpQp uniformly for all p . For any fixed finite extension of QpQp, we give an existential formula and a universal formula in the ring language which define the valuation ring.
Journal: Annals of Pure and Applied Logic - Volume 164, Issue 12, December 2013, Pages 1236–1246