94 citations · 113 across the 15 of their papers we have counts for
16 papers
Stable amalgamation over a predicate and the Gaifman property
Saharon Shelah, Alexander Usvyatsov
We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call…
On sample complexity of neural networks
Alexander Usvyatsov
We consider functions defined by deep neural networks as definable objects in an o-miminal expansion of the real field, and derive an almost linear (in the number of weights) bound…
Generic wide indiscernible sets
Alexander Usvyatsov
We prove that a wide Morley sequence in a wide generically stable type is isometric to the standard basis of an space for some .
Classification over a predicate -- the general case. Part I -- structure theory
Saharon Shelah, Alexander Usvyatsov
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier…
Minimal types in stable Banach spaces
Saharon Shelah, Alexander Usvyatsov
We prove existence of wide types in a continuous theory expanding a Banach space, and density of minimal wide types among stable types in such a theory. We show that every minimal…
Strict independence
Itay Kaplan, Alexander Usvyatsov
We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular it follows from our investig…