Abstract
This chapter focuses on facts in common between the random and Cohen extensions. Continuum Hypothesis can be violated by adding Cohen generic reals and by adding random reals. These generic extensions are similar in many respects but differ greatly in their effects on measure and category. The chapter presents a unified treatment of both extensions simultaneously. Their properties can actually be derived from some abstract properties shared by the ideal of meagre sets and the ideal of null set. The chapter presents results that also apply to the extensions arising from any other ideals that share these properties.
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