4 papers · 1 filter
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…
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…