[FOM] R: Re: Seeking sage advice on terminology

iao271055 at libero.it iao271055 at libero.it
Wed Aug 7 04:04:02 EDT 2013

Dear Colin,
How about using the traditional distinction between elementary and non-elementary proofs of a mathematical assertion A? If by 'elementary proof of an assertion A belonging to the language of a mathematical theory T' we mean a proof of A carried out entirely within T, it seems to me that a proof of 'T |- A' is not elementary (in the above sense).  At present we only have a non-elementary proof of Fermat Last Theorem.
Best wishes,
Gianluigi Oliveri

----Messaggio originale----

Da: frode.bjordal at ifikk.uio.no

Data: 3-ago-2013 12.39

A: "Foundations of Mathematics"<fom at cs.nyu.edu>

Ogg: Re: [FOM] Seeking sage advice on terminology

I now write thesis for theses of the system and theorem for results about the system.

Professor Dr. Frode Bjørdal
Universitetet i Oslo Universidade Federal do Rio Grande do Nortequicumque vult hinc potest accedere ad paginam virtualem meam

2013/8/1 Nik Weaver <nweaver at math.wustl.edu>


I'm writing a book on forcing right now and have a similar issue.

The terminological distinction I am using is "theorem" versus

"metatheorem".  Once that terminology is set up I don't find it

necessary to use different terms for proof of theorems and proofs

of metatheorems.

If saying "FLT is a theorem (of PA)" and "PA |- FLT is a metatheorem

(of your metatheory)" doesn't solve your problem, perhaps you could

use the term "metaproof" for a proof in the metatheory.


When I write about proofs of FLT I always have trouble finding a graceful

terminology to distinguish proving FLT in PA versus proving in proof theory

that PA |- FLT.

I don't mean the conceptual distinction is difficult.  I mean I'd like

a cleaner terminology for it so i don't keep using "proof" to mean two

different things.  Maybe the literature I have been reading does have

a solution but if so I have not absorbed it.


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