Cahiers du Centre de Logique,
vol. 17
References
Roland
Hinnion and Thierry
Libert (eds), One Hundred Years of Axiomatic Set Theory
volume 17 of the Cahiers du Centre de logique, AcademiaBruylant,
LouvainlaNeuve (Belgium), 2010, 110 pages.
ISBN 9782872099740
This Cahier can be ordered from the publisher AcademiaL'Harmattan.
Summary
In response to the paradoxes of naive set theory, axiomatic foundations
for set theory and mathematics were proposed in 1908 by Ernst
Zermelo and Bertrand Russell.
This Cahier is devoted to settheoretic systems related to Zermelo's,
such as fragments of ZF, but also to Russell's (Simple Type Theory)
or even to Quine's “New Foundations”  after all, Quine
was born in 1908 too! It is essentially made of papers presented
at the homonymous conference that was organized by the editors
in Brussels on 3031 October 2008. These have been arranged so
that this volume can virtually be divided into two bundles of
papers: one discussing systems related to Zermelo's (Halbeisen,
Pettigrew, Mathias, Hinnion), the other dealing more specifically
with systems related to type theory and stratification (Hinnion,
Kaye, Forster). That barrier is permeable and researchers in those
fields would be the first to admit that any strict division is
futile. More important is the fact that all the papers that compose
this volume will finally treat of key notions in the axiomatization
of set theory, such as choice (Halbeisen), infinity (Pettigrew),
foundation (Hinnion), typing (Forster), as well of famous model
constructions, such as forcing (Mathias) and models with automorphisms
(Kaye).
Table of contents
Halbeisen, L. 
Comparing cardinalities in Zermelo's system 


Pettigrew, R. 
The foundations of arithmetic in finite bounded Zermelo
set theory 1 

Mathias, A. R. D. 
Set forcing over models of Zermelo or Mac Lane 

Hinnion, R. 
Some specificities of Zermelo's Set Theory 

Kaye, R. W. 
Automorphisms and constructions of models of set theory 

Kaye, R. W. 
On the bounding lemma for KF 

Forster, T. E. 
The ParisHarrington Theorem in an NF context 






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