Kurt Gödel. Metamathematical Results on Formally Undecidable Propositions: Completeness vs. Incompleteness
Kurt Gödel. Metamathematical Results on Formally Undecidable Propositions: Completeness vs. Incompleteness

Summary/Abstract: Kurt Godel was a solitary genius, whose work influenced all the subsequent developments in mathematics and logic. The striking fundamental results in the decade 1929 1939 that made Godel famous are the completeness of the first order predicate logic proof calculus, the incompleteness of axiomatic theories containing arithmetic, and the consistency o f the axiom of choice and the continuum hypothesis with the other axioms of set theory. During the same decade Godel made other contributions to logic, including work on intuitionism and computability, and later, under the influence of his friendship with Einstein, made a fundamental contribution t o the theory of spacetime. In this article I am going to summarise the most outstanding results on incompleteness and undecidability that changed the fundamental views of modern mathematics.

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