computable

TL;DR: The paper shows that there is no solution to a differential equation satisfying an initial condition using a function uniformly continuous in a rectangle centered at the origin.

Abstract: This paper shows that, in recursive analysis, there is a function /(JC, y), uniformly continuous in a rectangle R centered at the origin, such that the differential equation dyjdx = f(x, y(x)) has no solution y(x) satisfying the initial condition y(0) = 0. This carefully written and important paper gives a clear and definitive account of the Russian constructivist view of the foundations of mathematics. Having described the nature of con structive objects and statements about them, and clarified the notions of identity and potential infinity, the author attacks the problem of giving constructive meaning to the usual logical connectives. For conjunction, disjunction, and existential quantification we need an intuition of generality of the basis of limited experience. Negation and implication are even more intricate. For recursive and recursively enumerable statements a clear interpretation can be given. For more general statements the notation of derivability in a formal system must be used. Suitable formal systems are introduced in the two papers whose review follows.