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4 papers
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…
From Schanuel's Conjecture to Shapiro's Conjecture
P. D'Aquino, A. Macintyre, G. Terzo
In this paper we prove Shapiro's 1958 Conjecture on exponential polynomials, assuming Schanuel's Conjecture.