Cohen forcing List of forcing notions

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in cohen forcing (named after paul cohen) p set of functions finite subset of ω2 × ω {0,1} , p < q if p



⊇


{\displaystyle \supseteq }

q.


this poset satisfies countable chain condition. forcing poset adds ω2 distinct reals model; poset used cohen in original proof of independence of continuum hypothesis.


more generally, 1 can replace ω2 cardinal κ construct model continuum has size @ least κ. here, restriction κ not have cofinality ω.







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