Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
goedels_incompleteness_theorems [2007-10-19 14:20] – 192.168.1.34goedels_incompleteness_theorems [2007-10-19 14:21] (current) – 192.168.1.34
Line 1: Line 1:
- 
-<pre> 
  
 Gödel's first incompleteness theorem, perhaps the single most celebrated result in mathematical logic, states that: Gödel's first incompleteness theorem, perhaps the single most celebrated result in mathematical logic, states that:
Line 9: Line 7:
  
 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.  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. 
- 
-</pre> 
  
 http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
  

User Tools

Page Tools

Site Tools