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Metamathematical results on formally undecidable propositions : Completeness vs
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gödel, Kurt |
| Copyright Year | 2005 |
| Abstract | 1. Life and work Kurt Gödel 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 Gödel famous are the completeness of the first-order predicate logic proof calculus, the incompleteness of axiomatic theories containing arithmetic, and the consistency of the axiom of choice and the continuum hypothesis with the other axioms of set theory. During the same decade Gödel 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 to the theory of space-time. In this article I am going to summarize the most outstanding results on incompleteness and undecidability that changed the fundamental views of modern mathematics. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.cs.vsb.cz/duzi/goedel.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
