Teorema ketaklengkapan Gödel: Perbedaan antara revisi

 

Now comes the trick: The notion of provability itself can also be encoded by Gödel numbers, in the following way. Since a proof is a list of statements which obey certain rules, the Gödel number of a proof can be defined. Now, for every statement ''p'', one may ask whether a number ''x'' is the Gödel number of its proof. The relation between the Gödel number of ''p'' and ''x'', the potential Gödel number of its proof, is an arithmetical relation between two numbers. Therefore there is a statement form Bew(''y'') that uses this arithmetical relation to state that a Gödel number of a proof of ''y'' exists:

The name '''Bew''' is short for ''beweisbar'', the German word for "provable"; this name was originally used by Gödel to denote the provability formula just described. Note that "Bew(''y'')" is merely an abbreviation that represents a particular, very long, formula in the original language of ''T''; the string "Bew" itself is not claimed to be part of this language.