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Reference.org
PCF theory
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<p>PCF theory is the name of a <a href="/facts/Mathematics/pxTouaz4">mathematical</a> theory, introduced by Saharon Shelah (1978), that deals with the <a href="/facts/Cofinality/cC8dl3oW">cofinality</a> of the <a href="/facts/Ultraproduct/d4cT10hd">ultraproducts</a> of <a href="/facts/Ordered_set/qb4a3FAX">ordered sets</a>. It gives strong upper bounds on the cardinalities of <a href="/facts/Power_set/FVuf8PDD">power sets</a> of <a href="/facts/Regular_cardinal/wrGvPz2c">singular</a> <a href="/facts/Cardinal_number/ccoKwU4R">cardinals</a>, and has many more applications as well. The abbreviation "PCF" stands for "possible <a href="/facts/Cofinality/cC8dl3oW">cofinalities</a>". </p>