The Rasiowa–Sikorski lemma is a result in the field of mathematical logic, particularly in set theory and model theory. It provides a criterion for determining whether a certain kind of subset exists in a model of set theory. The lemma is named after the mathematicians Helena Rasiowa and Andrzej Sikorski, who contributed to the field of logic in the mid-20th century.
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If is a countable transitive model, , and , enumerate the dense subsets of belonging to and recursively choose a decreasing sequence starting below that meets each one. Its upward closure is a generic filter over containing .