3 citations · 4 across the 6 of their papers we have counts for
8 papers
Skew-invariant curves and the algebraic independence of Mahler functions
Alice Medvedev, Khoa Dang Nguyen, Thomas Scanlon
For a positive rational number different from one, we say that the Puisseux series is -Mahler of n…
Variations on the Feferman-Vaught Theorem, with applications to
Alice Medvedev, Alexander Van Abel
Using the Feferman-Vaught Theorem, we prove that a definable subset of a product structure must be a Boolean combination of open sets, in the product topology induced by giving eac…
Multiplicative groups of fields and hereditarily irreducible polynomials
Alice Medvedev, Ramin Takloo-Bighash
In this paper we explore the concept of {\em good heredity} for fields from a group theoretic perspective. Extending results from \cite{alice}, we show that several natural familie…
ACFA
Alice Medvedev
We show that many nice properties of a theory follow from the corresponding properties of its reducts to finite subsignatures. If is a directed family of…
Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy
Uri Andrews, Alice Medvedev
We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all c…
Grouplike minimal sets in ACFA and in T_A
Alice Medvedev
This paper began as a generalization of a part of the author's PhD thesis about ACFA and ended up with a characterization of groups definable in T_A. The thesis concerns minimal fo…
An invitation to model-theoretic Galois theory
Alice Medvedev, Ramin Takloo-Bighash
We carry out some of Galois's work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by…
Invariant varieties for polynomial dynamical systems
Alice Medvedev, Thomas Scanlon
We study algebraic dynamical systems (and, more generally, -varieties) given by coordinatewise univariate polynomials…