4 citations · 5 across the 6 of their papers we have counts for
6 papers
Strongly minimal reducts of valued fields
Piotr Kowalski, Serge Randriambololona
We prove that if a strongly minimal non-locally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the…
O-minimal structures: low arity versus generation
Serge Randriambololona
We show that an analogue of the Hilbert's Thirteenth Problem fails in the real subanalytic setting.Namely we prove that, for any integer , the o-minimal structure generated by r…
Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation
Serge Randriambololona
This article presents two constructions motivated by a conjecture of L. van den Dries and C. Miller concerning the restricted analytic field with exponentiation. The first construc…
Tameness of holomorphic closure dimension in a semialgebraic set
Janusz Adamus, Serge Randriambololona
Given a semianalytic set S in a complex space and a point p in S, there is a unique smallest complex-analytic germ at p which contains the germ of S, called the holomorphic closure…
Some (non-)elimination results for curves in geometric structures
Serge Randriambololona, Sergei Starchenko
We show that the first order structure whose underlying universe is and whose basic relations are all algebraic subset of does not have quantifier elimina…
Tameness of complex dimension in a real analytic set
Janusz Adamus, Serge Randriambololona, Rasul Shafikov
Given a real analytic set X in a complex manifold and a positive integer d, denote by A(d) the set of points p in X at which there exists a germ of a complex analytic set of dimens…