[FOM] Reverse Mathematics and Analysis

[Harvey Friedman]

On 10/29/04 12:44 PM, "D.R. MacIver" <drm39 at cam.ac.uk> wrote:

> Hi,
> 
> I'm in the process of trying to put together a proposal (and in particular
> a reading list) for a part III essay on the foundations of analysis:
> Basically how it depends on the underlying set theoretic axioms (I don't
> want to investigate anything too wild here. Standard logical systems and
> working in ZF + stuff).
> 
> It's been suggested that I take a look at reverse mathematics, and how much
> if any of it I wanted to include. At the moment I know essentially nothing
> about it (pretty much what's in the wikipedia entry and nothing else), so
> I'd appreciate it if you could give me some pointers in the right
> direction: What books would be good to learn about it, and to get a feel
> for the subject. Ideally with at least some nod in the direction of
> analysis kept in mind, as I'd imagine the theory has a rather different
> character when looking at, for example, number theory or algebra (of course
> it might not. As I said, I simply don't know much about it).
> 

The standard book is Steve Simpson's

Subsystems of Second Order Arithmetic.

The book is pretty comprehensive and well written.

Steve, let us know here on the FOM what the republication schedule of this
book is.

Also, there is an upcoming Reverse Mathematics special session at the
Atlanta meetings. Jeff Hirst - can you post info about this meeting here on
the FOM?

Harvey Friedman