图 书 馆
可计算性与不完全性Computability And Incompleteness |
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| 课程网址: | http://videolectures.net/ssll09_martin_cai/ |
| 主讲教师: | Errol Martin |
| 开课单位: | EP马丁咨询公司 |
| 开课时间: | 2009-04-01 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | In these lectures we cover the following topics: Computability and Recursive Functions, Proof that exactly the partial recursive functions are computable, Gödel’s Incompleteness Theorems, Löb's Theorem.These very deep and very powerful results in metalogic from the 1930s were unexpected. They arose in a context in which it was expected that a finitary proof of consistency of arithmetic would shortly be forthcoming. This followed the proposal by the mathematician David Hilbert (1862-1943) for the complete axiomatisation and formalisation of all mathematical knowledge and proofs. Although committed to formal methods, many of Hilbert’s proofs were existential in nature, which ran counter to the finitistic, constructivist methods of mathematics. To deal with this criticism, Hilbert proposed that the formal methods program should establish that all of the “Ideal” existential arguments could in principle be replaced by “Real” constructive arguments, by showing some sort of conservation result. However, the incompleteness results showed that this ‘program’ could not be carried out in a simple way. |
| 关 键 词: | 可计算性; 递归函数; 公理化 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-09-23：cwx |
| 阅读次数: | 51 |