Re: Goedel's undecidable G

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? Note also that G\"odel used a
version of Whitehead and Russell's type theory.

To express G a long sequence of definitions is used and the G that
results is _not_ in the language of PA. G\"odel's original paper is
readily available [1, 2] so you could always take it and unwind the
definitions back to the language of (G\"odel's version of) Whitehead and
Russell's type theory.

You can find a version using Peano in [3]--38 pages from the definition
of PA's language (using + and .) to G.

[1] Jean van Heijenoort, ed, From Frege to G\"odel, A Source Book in
Mathematical Logic, 1879-1931, Harvard UP.

[2] Martin Davis, ed, The Undecidable. Basic Papers on Undecidable
Propositions, Unsolvable Problems and Computable Functions, Raven
Press.

[1] is printed to a higher quality and has useful introductory notes.

[3] Elliott Mendelson, Introduction to Mathematical Logic, 2 ed, D van
Nostrand.

--
I don't know who you are Sir, or where you come from,
but you've done me a power of good.
.

Relevant Pages

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