There is a useful method for constructing models of set theory with the continuum arbitrarily large, involving iterated forcing with symmetric systems of models as side conditions. It turns out that a natural variation of this method can be used to produce forcing constructions giving rise to models of the Continuum Hypothesis. Unlike the case with the classical approaches to preserving CH, this new method produces forcing notions which actually add new reals, but only a small number of them. I will give a gentle introduction to this method, focusing on some of its applications.
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