Show pageOld revisionsBacklinksBack to top You've loaded an old revision of the document! If you save it, you will create a new version with this data. Media Files <quote> Gödel's first incompleteness theorem, perhaps the single most celebrated result in mathematical logic, states that: For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Gödel's second incompleteness theorem can be stated as follows: For any formal recursively enumerable (i.e. effectively generated) theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent. </quote> http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Please fill all the letters into the box to prove you're human. Please keep this field empty: SavePreviewCancel Edit summary Note: By editing this page you agree to license your content under the following license: CC Attribution-Share Alike 4.0 International goedels_incompleteness_theorems.1192803627.txt.gz Last modified: 2007-10-19 14:20by 192.168.1.34