On 12 Jun 2013, at 20:49, meekerdb wrote:
On 6/12/2013 1:57 AM, Bruno Marchal wrote:
Arithmetic is large, and I do not know of any theorem in math which
is not a theorem in arithmetic, except in mathematical logic, and
universal algebra, which are typically "meta-"mathematics.
What about theorems in calculus and topology?
Most, if not all, are theorems of arithmetic in disguise. Few math go
really beyond PI-1 or Pi_2 arithmetical complexity, when you study
their logical complexity. Only category and set theory go much beyond,
and genuinely go beyond arithmetical complexity.
I could say more on this when I have more time, but it requires some
amount of mathematical logic.
Macintyre wrote papers on this, and Torkel Franzen made a similar
point in his book "inexhaustibility".
Some other people makes this points trivial, but only by a *misuse* of
comp, note.
Bruno
Brent
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