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A model of      ZFC + 2 ℵ  0 = ℵ  2 {\text {ZFC}} + {2^{\aleph _0}} = {\aleph _2}       is constructed which is minimal with respect to being a model of      ¬  CH \neg {\text {CH}}      . Any strictly included submodel of      ZF {\text {ZF}}       (which contains all the ordinals) satisfies      CH {\text {CH}}      . In this model the degrees of constructibility have order type      ω  2 {\omega _2}      . A novel method of using the diamond is applied here to construct a countable-support iteration of Jensen’s reals: In defining the      α  th \alpha {\text {th}}       stage of the iteration the diamond "guesses" possible      β  &gt; α  \beta &gt; \alpha       stages of the iteration.

A minimal model for ¬𝐶𝐻: iteration of Jensen’s reals