10 citations · 59 across the 20 of their papers we have counts for
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Algebraic types in Zilber's exponential field
Vahagn Aslanyan, Jonathan Kirby
We characterise the model-theoretic algebraic closure in Zilber's exponential field. A key step involves showing that certain algebraic varieties have finite intersections with cer…
The Existential Closedness and Zilber-Pink Conjectures
Vahagn Aslanyan
In this paper we survey the history of, and recent developments on, two major conjectures originating in Zilber's model-theoretic work on complex exponentiation -- Existential Clos…
Independence relations for exponential fields
Vahagn Aslanyan, Robert Henderson, Mark Kamsma +1
We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, sho…
A closure operator respecting the modular -function
Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby
We prove some unconditional cases of the Existential Closedness problem for the modular -function. For this, we show that for any finitely generated field we can find a "conveni…
Differential Existential Closedness for the -function
Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby
We prove the Existential Closedness conjecture for the differential equation of the -function and its derivatives. It states that in a differentially closed field certain equati…
Existentially closed De Morgan algebras
Vahagn Aslanyan
We show that the theory of De Morgan algebras has a model completion and axiomatise it. Then we prove that it is -categorical and describe definable and algebraic closure…
Ax-Schanuel and strong minimality for the -function
Vahagn Aslanyan
Let be a differentially closed field of characteristic with field of constants . In the first part of the paper we explore the connection…
Adequate Predimension Inequalities in Differential Fields
Vahagn Aslanyan
In this paper we study predimension inequalities in differential fields and define what it means for such an inequality to be \emph{adequate}. Adequacy was informally introduced by…
Ax-Schanuel type theorems and geometry of strongly minimal sets in differentially closed fields
Vahagn Aslanyan
Let be a differentially closed field. In this paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differentia…
Ax-Schanuel for Linear Differential Equations
Vahagn Aslanyan
We generalise the exponential Ax-Schanuel theorem to arbitrary linear differential equations with constant coefficients. Using the analysis of the exponential differential equation…
Definability of derivations in the reducts of differentially closed fields
Vahagn Aslanyan
Let be a differentially closed field. We consider the question of definability of the derivation in reducts of of the form $\mathc…