This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning and is sufficiently detailed to provide an introduction to research in this area.Expand

This work presents a mathematical definition of an analog generable function of a real variable in terms of a simultaneous set of nonlinear differential equations possessing a "domain of generation," which includes functions generated by existing general-purpose analog computers.Expand

Two theorems are proved that there exists an axiomatizable, essentially undecidable theory in standard formalization such that all axiom atizable extensions of are finite extensions.Expand

A rough statement of the main result is given, which states that the propagation u(x, y, z, t) of a wave can be noncomputable in any neighborhood of any point of D even though the initial conditions which determine the wave propagation uniquely are computable.Expand

Introduction. In this work we discuss recursive mappings between theories which preserve deducibility, negation and implication. Roughly, we prove that any two axiomatizable theories containing a… Expand