72 citations · 140 across the 39 of their papers we have counts for
7 papers · 1 filter
Logarithmic--exponential preparation in sharply o-minimal structures
Gal Binyamini, Oded Carmon, Dmitry Novikov
We develop a complex-analytic approach to the model theory of the (real) unrestricted exponential. As a consequence we derive sharp forms of many of the foundational results for th…
Complex cells in sharply o-minimal structures
Gal Binyamini, Oded Carmon, Dmitry Novikov
We extend the theory of complex cells introduced by Binyamini and Novikov to the sharply o-minimal setting, obtaining cellular preparation and parameterization theorems which are p…
Sharply o-minimal structures and sharp cellular decomposition
Gal Binyamini, Dmitri Novikov, Benny Zak
Sharply o-minimal structures (denoted \so-minimal) are a strict subclass of the o-minimal structures, aimed at capturing some finer features of structures arising from algebraic ge…
Wilkie's conjecture for Pfaffian structures
Gal Binyamini, Dmitry Novikov, Benny Zack
We prove an effective form of Wilkie's conjecture in the structure generated by restricted sub-Pfaffian functions: the number of rational points of height lying in the transcen…
Effective cylindrical cell decompositions for restricted sub-Pfaffian sets
Gal Binyamini, Nicolai Vorobjov
The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format $\mathcal…
Wilkie's conjecture for restricted elementary functions
Gal Binyamini, Dmitry Novikov
We consider the structure obtained from by adjoining the restricted exponential and sine functions. We prove Wilkie's conjectu…
The Pila-Wilkie theorem for subanalytic families: a complex analytic approach
Gal Binyamini, Dmitry Novikov
We present a complex analytic proof of the Pila-Wilkie theorem for subanalytic sets. In particular, we replace the use of -smooth parametrizations by a variant of Weierstrass…