[FOM] Ultrafinitism - help!

Vaughan Pratt pratt at cs.stanford.edu
Wed Jan 23 02:33:47 EST 2013

Dear Thomas,

While I count myself more as an observer than an enthusiast on this 
topic, if all your faculty office needs is a couple of paragraphs then


and its talk page (the Talk tab at upper left) should supply more than 
enough material for that purpose.

That should also suffice for a resourceful student, but if not suggest 
in addition MathOverflow,


Less well publicized are my own modest contributions, which can be seen at


which introduces the notion of "Jumpy-In Syndrome" (JIS, definite 
infinite vs. indefinite finite), and


mentioning several ideas including Rohit Parikh's generous upper bound 
of 2^{1000} on ultrafinite numbers, which as far as I know has not been 
improved in the meantime (but check with Rohit who is good at answering 

More than a decade earlier, Robert Tragesser held forth at considerable 
length on this topic at


See in particular his section II, "CORE LITERATURE ON ULTRAFINITISM". 
This was Tragesser's Part I of what was to have had a Part II, which 
however I've so far been unable to locate.

Best regards,
Vaughan Pratt

On 1/22/2013 4:24 AM, T.Forster at dpmms.cam.ac.uk wrote:
> I have a student here who wants to write a fourth year (Part III) essay
> on ultrafinitism, a topic of which my knowledge is, as it were,
> *ultra*finite. Within 10 days i have to supply the faculty office a
> couple of paragraphs saying what the student should read and what sort
> of topics the essay should cover, which results should be proved, and so
> on.
>      Any enthusiasts out there who can get me out of this hole?
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