Cahiers du Centre de Logique 


Version française

Cahiers du Centre de Logique, vol. 13


Olivier Esser, Une théorie positive des ensembles
volume 13 of the Cahiers du Centre de logique, Academia-Bruylant, Louvain-la-Neuve (Belgium), 2004, 117 pages
ISBN 2-8729-687-6, 18 euros

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


The point of departure for Positive theories of sets is the observation that all definitions of paradoxical sets exploit negation. The proposal is that - for a suitable notion of positive - every positive formula should determine a set.

Olivier Esser starts with an existing positive theory enriched with an axiom scheme that endows each class with a "closure". He shows that the resulting theory interprets the theory of Kelley-Morse together with the axiom "the class of ordinals is ramifiable", and conversely.

His results show clearly that the orthodox theories have excluded too many sets. By eschewing solely what causes problems in the paradoxes - namely the use of negation in comprehension axioms - he recovers not only the sets of the usual theories but also lots of others that one had no reasonable motive to exclude.



17 l 16 l 15 l 14 l 12 l 11 l 10 l 9 l 8 l 7 l 6 l 5 l 4 l 3 l 2 l 1



October 23, 2015