منابع مشابه
Imaginaries in Real Closed Valued Fields I
We investigate the embeddings of the value group and residue field of a real closed valued field A in Aeq via quantifier elimination in a three sorted language. We classify the one types of field elements in a real closed valued field. Finally, we investigate some of the linear structure in Aeq induced by the valuation ring V and introduce the geometric sorts. In a subsequent paper we show that...
متن کاملImaginaries in Real Closed Valued Fields II
The paper shows elimination of imaginaries for real closed valued fields to the geometric sorts which were introduced in the [6]. We also show that this result is in some sense optimal.
متن کاملImaginaries in algebraically closed valued fields
These notes are intended to accompany the tutorial series ‘Model theory of algebraically closed valued fields’ in the Workshop ‘An introduction to recent applications of model theory’, Cambridge March 29–April 8, 2005. They do not contain any new results, except for a slightly new method of exposition, due to Lippel, of parts of the proof of elimination of imaginaries, in Sections 8 and 9. They...
متن کاملDefinable sets in algebraically closed valued fields: elimination of imaginaries
It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K of certain definable R-submodules of K (for all n ≥ 1). The proof involves the development of a theory of independence for unary types, which play the role of 1-types, followed by an analysis of germs of definabl...
متن کاملImaginaries in pairs of algebraically closed fields
We consider the theory (ACFp)P of pairs F < K of algebraically closed fields of a given characteristic p. We exhibit a collection of additional sorts in which this theory has geometric elimination of imaginaries. The sorts are essentially of the form ∪a∈B(F )Va(K)/Ga(F ), where G, V,B are varieties over the prime field G a group scheme over B and V is a scheme over B (both with irreducible fibr...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2006
ISSN: 0168-0072
DOI: 10.1016/j.apal.2005.05.014