Théories paraconsistantes des ensembles

Newton CA da Costa, Jean-Yves Béziau


Paraconsistency is a way to develop set theory with a Russellian set. We present here two main paraconsistent set theories, one similar to Quine's NF and the other one analogous to Church theory with a universal set. Basic properties of Russell set are studied. Some striking features of the paraconsistent relation of membership are described. The paper is a synthesis of old results (by da Costa, Arruda, Batens, Sylvan) and new ones (by da Costa, Béziau, Wertheyser).

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