Beginning in the mid-1950s, P�ter applied recursive function theory to computers.
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Recursive function theory / lambda calculus?
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These papers helped to found the modern field of recursive function theory as a separate area of mathematical research.
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For example we can encode Markov algorithms, or Turing machines into natural numbers and thereby prove that the expressive power of recursive function theory is no less than that of the former machine-like formalizations of algorithms.
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It is the ability of self homeomorphism as well as the ability to embed every space into such a space, denoted Scott continuous, as previously described which allows Scott's topology to be applicable to logic and recursive function theory.
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Proofs which mention computer programs have to be stated in the mathematician's preferred language, which is called " recursive function theory " which is " purposefully " obscure : it is designed to look as little as possible like ordinary computer programs.
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