Cohen's Forcing

Cohen forcing is a mathematical technique used in set theory to expand a universe of mathematical objects, like adding new real numbers, without altering existing basic properties. It involves carefully constructing a structured process (called a forcing notion) that introduces these new elements in a controlled way, ensuring consistency. Think of it like extending an existing mathematical universe to include new points without changing its fundamental characteristics—similar to adding new paths in a network without disrupting its overall structure. Cohen forcing is a foundational tool for proving that certain mathematical statements are independent of standard set theory.