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**publisher and metadata sources**).PROOF. Let 0,CNN be a set of cardinality c of functions of incomparable Turing degree [2]. Let A be a family of subsets of (, of cardinality 2c which are incomparable with respect to inclusion (such… Continue Reading

In this paper we show how the assumption of the generalized continuum hypothesis (GCH) can be removed or partially removed from proofs in Zermelo-Frankel set theory (ZF) of statements expressible in… Continue Reading

where [u] is the uth finite set in some recursive coding of finite sets. Since A is 21 (1) shows that any 4 partial recursive in 6A has 21 graph; furthermore since A is many-one complete for 21 sets… Continue Reading