[FOM] PA inconsistencies

Richard Kimberly Heck richard_heck at brown.edu
Tue Aug 21 21:20:12 EDT 2018

On 08/19/2018 12:38 PM, Harvey Friedman wrote:
>> FOM Readership: what are the main references for "mathematics without
>> exponentiation" and how far has it gotten?

> I meant an depth development of actual mathematics, (analysis,
> algebra, number theory, differential equations, topology, geometry,
> group theory, etc,.), not computational complexity developments or
> math logic developments.

It's a few years old now (2013), but there is a nice paper by Fernando
and Gilda
Ferreira, "Interpretability in Robinson's Q", that summarizes the
results that were
then known. This includes some new results, also, in the paper on
of fragments of analysis. This includes theories capable of proving e.g.
intermediate value theorem and the fundamental theorem of the calculus.

Of course, there are serious limits to what one can do in this
direction. But it is,
as they say, striking how much one can do here.


Richard Kimberly (Riki) Heck
Professor of Philosophy
Brown University

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