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goedels_incompleteness_theorems [2007-10-19 14:20] – created 192.168.1.34goedels_incompleteness_theorems [2007-10-19 14:20] – 192.168.1.34
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 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:
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 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. 
  
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 http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
  
  • goedels_incompleteness_theorems.txt
  • Last modified: 2007-10-19 14:21
  • by 192.168.1.34