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Realizability algebras II : new models of ZF + DC (1007.0825v4)
Published 6 Jul 2010 in math.LO and cs.LO
Abstract: Using the proof-program (Curry-Howard) correspondence, we give a new method to obtain models of ZF and relative consistency results in set theory. We show the relative consistency of ZF + DC + there exists a sequence of subsets of R the cardinals of which are strictly decreasing + other similar properties of R. These results seem not to have been previously obtained by forcing.