collaborators

7 papers

math.LO2026

Relative stability, relative categoricity and internal covers

Mostafa Mirabi, Anand Pillay

Let be a countable complete theory with a distinguished unary predicate , and let be the theory of the -parts of models of with the induced structure. is…

math.LO2026

Definable Galois theory for bimeromorphic geometry

Rahim Moosa, Anand Pillay

The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex space…

math.LO2026

Remarks on relative categoricity

Anand Pillay

The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A s…

math.LO2026

On groups definable in geometric fields with generic derivations

Anand Pillay, Françoise Point, Silvain Rideau-Kikuchi

We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretab…

math.LO2026

An arithmetic algebraic regularity lemma

Anand Pillay, Atticus Stonestrom

We give an 'arithmetic regularity lemma' for groups definable in finite fields, analogous to Tao's 'algebraic regularity lemma' for graphs definable in finite fields. More specific…

math.LO2026

On groups definable in -adically closed fields

Anand Pillay, Ningyuan Yao, Zhentao Zhang

This paper is about the / decomposition for groups definable in -adically closed fields. It is proved that for definably amenable, has a definable normal $…