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Computability in analysis and physics
This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning and provides an introduction to research in this area. Expand
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The wave equation with computable initial data such that its unique solution is not computable
We consider the three-dimensional wave equation. It is well known that the solution U(X, y, z, t) is uniquely determined by two initial conditions: the values of u and au/at at time t = 0. OurExpand
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This paper treats in a systematic way the following question: which basic constructions in real and complex analysis lead from the computable to the noncomputable, and which do not? The topicsExpand
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Axiomatizable Theories with Few Axiomatizable Extensions
In this paper we prove two theorems. They answer questions raised by Myhill in 1956. (We recall the well-known fact that Myhill's invention of the maximal set in 1956 [2] stemmed from his attempt toExpand
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The Wave Equation with Computable Initial Data Whose Unique Solution Is Nowhere Computable
We give a rough statement of the main result. Let D be a compact subset of ℝ3× ℝ. The propagation u(x, y, z, t) of a wave can be noncomputable in any neighborhood of any point of D even though theExpand
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Effectively Extensible Theories
  • M. B. Pour-El
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 26 April 1968
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