Day4 - Hilberts Belief All mathematics could be developed within a formal system that allowed the mechanical creation and checking of proofs Dec 2

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10/4/11 Dec 2, © UCF (Charles E. 11 Hilbert’s Belief All mathematics could be developed within a formal system that allowed the mechanical creation and checking of proofs.
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10/4/11 Dec 2, © UCF (Charles E. 22 Gödel In 1931 he showed that any first order theory that embeds elementary arithmetic is either incomplete or inconsistent. He did this by showing that such a first order theory cannot reason about itself. That is, there is a first order expressible proposition that cannot be either proved or disproved, or the theory is inconsistent (some proposition and its complement are both provable). Gödel also developed the general notion of recursive functions but made no claims
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10/4/11 Dec 2, © UCF (Charles E. 33 Turing (Post, Church, Kleene) In 1936, each presented a formalism for computability. Turing and Post devised abstract machines and claimed these represented all mechanically computable functions. Church developed the notion of lambda-computability from
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This note was uploaded on 10/03/2011 for the course COT 5310 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Day4 - Hilberts Belief All mathematics could be developed within a formal system that allowed the mechanical creation and checking of proofs Dec 2

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