[FOM] strengths and weaknesses of Zermelo set theory

[A.R.D.Mathias]

Many of the topics about which Alex Dorin seeks information are treated in
detail in three of my papers:

for various forms of bounded Zermelo set theory, including the one
popularised by Saunders Mac Lane, see

"The Strength of Mac Lane Set Theory"

which came out in the Annals of Pure and Applied Logic in 2001:
for a summary see Mathematical Reviews, 2002g:03105;


for numerous models of Zermelo set theory, illustrating its weakness with
regard to recursive definitions, are constructed in my paper "Slim Models
of Zermelo Set Theory", which appeared in the Journal of Symbolic Logic in
the same year;

for other such models, and for remarks about finite axiomatisability, see 
"Weak Systems of Gandy, Jensen and Devlin", as yet unpublished but available
from my websites

http://www.dpmms.cam.ac.uk/~ardm
http://www.univ-reunion.fr/~ardm


A.R.D.Mathias,
   Professeur de Mathématiques Pures

Département de Mathématiques et Informatique,
Université de la Réunion
15, Avenue René Cassin BP 7151
97715 St Denis de la Réunion, Messagerie 9,
France

bureau:     00262 262 93 82 88
télécopie:  00262 262 93 82 60

On Fri, 3 Mar 2006, dorin alex wrote:
> Sirs !
>
> (FOM Digest, Vol 38, Issue 67) Harvey Friedman wrote:
>
> 1. Theory of classes, like NBG. It is finitely axiomatizable. One can
> actually write down the finitely many axioms, although it is messy. I
> know
> how to modify this somewhat and make it prettier.
>
> 2. Substantial fragments of ZFC. For example, bounded Zermelo set
> theory.
> This is also messy, but can be cleaned up somewhat.
>
> Please say where It can be read?
>
> Respectfully yours
> Alexander A. Dorin
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