 Intuitionistic Set Theory
John L. Bell
While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published. This may be the case in part because, as a form of higherorder intuitionistic logic  the internal logic of a topos  IST has been chiefly developed in a topstheoretic context. In particular, proofs of relative consistency with IST for mathematical assertions have been (implicitly) formulated in topos or sheaftheoretic terms, rather than in the framework of Heytingalgebravalued models, the natural extension to IST of the wellknown Booleanvalued models for classical set theory.
In this book I offer a brief but systematic introduction to IST which develops the subject up to and including the use of Heytingalgebravalued models in relative consistency proofs. I believe that IST, presented as it is in the familiar language of set theory, will appeal particularly to those logicians, mathematicians and philosophers who are unacquainted with the methods of topos theory.
5 February 2014
9781848901407
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