[FOM] Godel and PA

[Richard Heck]

On 03/04/2017 08:51 AM, Lawrence Paulson wrote:
> This may be a good time for another plug for "Finite sets and Gödel's
> incompleteness theorems" by S. Świerczkowski. He he fixes on the
> hereditarily finite sets (rather than natural numbers) as the
> foundation and presents a clear and reasonably formal development,
> with rather few gaps.

Thanks for mentioning this paper, which looks interesting. Another paper
in something like this tradition is Grzegorczyk's "Undecidability
Without Arithmetization", which bases the construction on a theory of
strings.

There is one claim Świerczkowski makes for his approach that is
definitely incorrect, viz, that it avoids the intensionality pointed out
by Feferman in "Arithmetization". The problem is not coding the notion
of a formal proof (which may be more natural in set theory) but deciding
how to represent infinite sets of axioms.

Richard Heck