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Computability in analysis and physics
TLDR
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.
Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)
TLDR
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.
COMPUTABILITY AND NONCOMPUTABILITY IN CLASSICAL ANALYSIS
TLDR
The purpose of this paper is to show which of the basic operations of analysis lead from the computable to the noncomputable, and which do not.
Axiomatizable Theories with Few Axiomatizable Extensions
TLDR
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.
The Wave Equation with Computable Initial Data Whose Unique Solution Is Nowhere Computable
TLDR
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.
Deduction-preserving "Recursive Isomorphisms" between theories
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
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