TITLE: Is there any forcing free proof for hard independence results?
QUESTION [9 upvotes]: We are forced to use forcing for almost all "hard" independence results such as: $Con(ZFC)\longrightarrow Con (ZFC+\neg CH) $. The question simply is:
Primary Question: Is there any "forcing free" proof for $Con(ZFC)\longrightarrow Con (ZFC+\neg CH) $ or $Con(ZF)\longrightarrow Con (ZF+\neg AC) $ or any other "hard" independence results? 
Secondary Question: Please list all "non simple" consistency results which have two proofs one by forcing and another without using it.

REPLY [6 votes]: Krivine realizability can be used to obtain independence results over $\mathsf{ZF}$. For instance, in Krivine's paper Realizability algebras II : new models of ZF + DC, Logical Methods in Computer Science 8 (1:10) p. 1-28 (2012), he constructs a realizability model in which $\mathsf{AC}$ fails in a pretty strong way: there is an infinite sequence of infinite subsets of $\mathbb{R}$ strictly decreasing in cardinality.