A key method in the usual proofs of the first incompleteness theorem is the arithmetization of the formal language, or Gödel numbering: certain natural numbers. Gödel Number. DOWNLOAD Mathematica Notebook. Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color. Gödel’s numbering system is a way of representing any sentence of the formal language as a number. That means that every sentence of the formal language.
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Godel numbering assigns a number to every formula. It appears to me that any encoding will do. However its numberring apparent, though I’m not sure how, that certain properties of the encoding used in Godel numbering are important for the purposes of the proof of the incompleteness theorem. In other words, if e.
Gödel numbering – Wikipedia
And then all the usual constructions and proofs can be done with the new scheme perhaps with greater elegance or more clumsily, depending on details as were done with the original scheme.
Home Questions Tags Users Unanswered. What are the formal properties of Godel numbering that are required to make it ‘work’?
What are these properties? Are they to do with effectiveness in some way?
logic – Confusion in Godel’s numbering for subscripts – Mathematics Stack Exchange
Mozibur Ullah 2, 10 And it is useful if the functions used to do the encoding are easily shown to be representable in the theory we are working with. I don’t think this is really a question about model-theory, as the incompleteness theorems are only loosely related goeel model theory perhaps ironically, the connection is by completeness theorem.
Still, there is some connection, so I have not removed the tag altogether, but if someone godwl with me, perhaps he will do just that.
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