Re: Goedel's undecidable G

Jim Spriggs napisal:
> LordBeotian wrote:
>> I want to see the explicit expression of G in the language of PA, is there
>> any web page where I can take a look to G?
> No, is my guess, because G will be _very_ complicated when expressed in
> the language of PA. Before saying more, I must admit to my ignorance
> about what the language of PA is. Does it just have a constant for zero
> and a function symbol for successor, or does it also have function
> symbols for addition and multiplication?
If formal theory has not multiplication there is no Goedel sentence
construction for it.

> To express G a long sequence of definitions is used and the G that
> results is _not_ in the language of PA.
You are wrong! Of course, and this is the clue, Goedel sentence
is a senntence of PA annd it is just ordinary theorem about natural
numbers! But simultaneously it may be interpreted as sentence about
itself...
Thanks
kazek
.

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