14 citations · 26 across the 13 of their papers we have counts for
14 papers
Imaginaries, products and the adele ring
Jamshid Derakhshan, Ehud Hrushovski
We describe the imaginary sorts of infinite products in terms of imaginary sorts of the factors. We extend the result to certain reduced powers and then to infinite products $\prod…
Axioms for Commutative Unital Rings elementarily Equivalent to Restricted Products of Connected Rings
Jamshid Derakhshan, Angus Macintyre
We give axioms in the language of rings augmented by a 1-ary predicate symbol with intended interpretation in the Boolean algebra of idempotents as the ideal of finite ele…
-adic model theory, -adic integrals, Euler products, and zeta functions of groups
Jamshid Derakhshan
We give a survey of Denef's rationality theorem on -adic integrals, its uniform in versions, the relevant model theory, and a number of applications to counting subgroups of…
Model Theory of Adeles and Number Theory
Jamshid Derakhshan
This paper is a survey on model theory of adeles and applications to model theory, algebra, and number theory. Sections 1-12 concern model theory of adeles and the results are join…
Solvability in groups with a chain condition on uniformly definable subgroups
Jamshid Derakhshan
We prove a structure theorem for periodic locally soluble groups satisfying a chain condition on intersections of relatively uniformly definable subgroups using results from the th…
Truncations of Ordered Abelian Groups
Paola D'Aquino, Jamshid Derakhshan, Angus Macintyre
The abstract will be added in due course.
Decidability Problems for Adele Rings and related restricted products
Jamshid Derakhshan, Angus Macintyre
We study elementary equivalence of adele rings and decidability for adele rings of general number fields. We prove that elementary equivalence of adele rings implies isomorphism of…
Model Theory of Adeles I
Jamshid Derakhshan, Angus Macintyre
We study the model theory of the ring of adeles of a number field. We obtain quantifier elimination results in the language of rings and some enrichments. We given consequences for…
Model theory of finite-by-Presburger Abelian groups and finite extensions of -adic fields
Jamshid Derakhshan, Angus Macintyre
We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multi…
Model Completeness for Henselian Fields with finite ramification valued in a -Group
Jamshid Derakhshan, Angus Macintyre
We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a -group, is model-complete in the language of ri…
Enrichments of Boolean Algebras: a uniform treatment of some classical and some novel examples
Jamshid Derakhshan, Angus Macintyre
We give a unified treatment of the model theory of various enrichments of infinite atomic Boolean algebras, with special attention to quantifier-eliminations, complete axiomatizati…
Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
Raf Cluckers, Jamshid Derakhshan, Eva Leenknegt +1
We give a definition, in the ring language, of Z_p inside Q_p and of F_p[[t]] inside F_p((t)), which works uniformly for all and all finite field extensions of these fields, an…
Some supplements to Feferman-Vaught related to the model theory of adeles
Jamshid Derakhshan, Angus Macintyre
We give foundational results for the model theory of the ring of finite adeles over a number field, construed as a restricted product of local fields. In contrast to Weispfenning w…
Uniform cell decomposition with applications to Chevalley groups
Mark N. Berman, Jamshid Derakhshan, Uri Onn +1
We express integrals of definable functions over definable sets uniformly for non-Archimedean local fields, extending results of Pas. We apply this to Chevalley groups, in particul…