Cahiers du Centre de Logique 


Cahiers du Centre de Logique, vol. 17


Roland Hinnion and Thierry Libert (eds), One Hundred Years of Axiomatic Set Theory
volume 17 of the Cahiers du Centre de logique, Academia-Bruylant, Louvain-la-Neuve (Belgium), 2010, 110 pages.
ISBN 978-2-87209-974-0

This Cahier can be ordered from the publisher Academia-L'Harmattan.


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 set-theoretic 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 30-31 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

  Cahier 17

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 Paris-Harrington Theorem in an NF context




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October 23, 2015