2 citations · 8 across the 6 of their papers we have counts for
7 papers · 1 filter
The model theory of residue rings of models of Peano Arithmetic: The prime power case
P. D'Aquino, A. Macintyre
In \cite{MacResField} the second author gave a systematic analysis of definability and decidability for rings , where is a model of Peano Arith…
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…
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…