Ax-Schanuel and strong minimality for the j-function

STRONG MINIMALITY AND THE j-FUNCTION

We show that the order three algebraic differential equation over Q satisfied by the analytic j-function defines a non-א0-categorical strongly minimal set with trivial forking geometry relative to the theory of differentially closed fields of characteristic zero answering a long-standing open problem about the existence of such sets. The theorem follows from Pila’s modular Ax-Lindemann-Weierstr...

Ax-Schanuel type theorems and geometry of strongly minimal sets in differentially closed fields

Let (K; +, ·,′ , 0, 1) be a differentially closed field. In this paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differential equation E(x, y) and the geometry of the set U := {y : E(t, y)∧ y′ 6= 0} where t is an element with t′ = 1. We show that certain types of predimension inequalities imply strong minimality and geometric triviality of U ....

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

On dp-minimality, strong dependence and weight

From the Minimality of J We Have That J = L 0 1. for Example, N L

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