Re: Looking for Undecidable Propositions in Systems without a certain amount of arthimetic.

Scott wrote:
Hi: In order to apply Godel's incompleteness theorem, we need "a
certain amount of arithmetic" in the formal system, which can be
loosely translated to natural numbers and a couple of basic rules
about addition and multiplication.

Does anyone know of undecidable
propositions in formal systems where natural numbers (or equivalent)
are not present; ie, the formal system does not meet the requirement
of "a certain amount of arithmetic"?

One simple example of such formal system is the basic group theory.
And this is an "under"-"a certain amount of arithmetic" example.
For an example of an "over" example, Godel's work in Incompleteness
hints to a place where I'd think you could try your luck: the collection
of formal systems with non-finite numbers of non-logical symbols. Imho.

--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")
.

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