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Kleene's research was on the theory of algorithms and recursive functions. He developed the field of recursion theory with Church, Gödel, Turing and others. He contributed to mathematical Intuitionism which had been founded by Brouwer.
His work on recursion theory helped to provide the foundations of theoretical computer science. By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions can be computed.
His best known books are Introduction to Metamathematics (1952) and Mathematical Logic (1967).
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