Modern Logic: Since GÖdel
Since GÖdel
The pace of development in logic picked up rapidly after Gödel's incompleteness theorems, and five branches emerged: set theory, model theory, proof theory, computability theory, and nonclassical logics.
Gödel's theorems were formulated for type theory, but this was soon displaced as the framework for mathematics by Zermelo-Frankel set theory with choice (ZFC). Gödel's theorems still apply, and imply the existence of set-theoretic statements that can be neither proved nor disproved. Gödel himself showed that Cantor's continuum hypothesis cannot be disproved, and conjectured that it cannot be proved, as was established in the 1960s by Paul Cohen......
This is a free excerpt of 100 words. This section contains 513 words.
Modern Logic: Since Gödel article
Read the rest of this article.
This article contains 68,831 words
(approx. 229 pages at 300 words per page).
Order our Classical logic Article
