Независимость принципа двойного дополнения множеств от схемы собирания в теории множеств с интуиционистской логикой.


V.Kh. Hakhanian


Let $ZFI_R + DCS$ is the intuitionistic set theory with the full list of set-theoretic axioms and the axiom of double complement of sets (DCS). There is an inner model of ZF (and ZFC) in our set theory; and this theory posesses the existential property ( Myhill and auther).
In 1993 1 also proved that the collection scheme is independent of our set theory . In present short note I give the proof independent sketch of DCS of $ZFI_R +$ collection - power axiom. I modife my model of realizabillity type (this model was constructed for the proof of consistency collection and DCS with $ZFI_R$) such that in the new model DCS is false and collection $+ ZFI_R$ is true ( I think, that power axiom also is true, but now I can’t to give such proof).
I will publish the full proof of this theorem in one of logic journals.