Английская Википедия:Chang's model
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In mathematical set theory, Chang's model is the smallest inner model of set theory closed under countable sequences. It was introduced by Шаблон:Harvs. More generally Chang introduced the smallest inner model closed under taking sequences of length less than κ for any infinite cardinal κ. For κ countable this is the constructible universe, and for κ the first uncountable cardinal it is Chang's model.
Chang's model is a model of ZF. Kenneth Kunen proved in Шаблон:Harvs that the axiom of choice fails in Chang's model provided there are sufficient large cardinals, such as uncountable many measurable cardinals.
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