Later, using Cohen's method of forcing, he proved several results on the consistency of various statements contradicting the axiom of choice.
For example, with J. D. Halpern he proved that the Boolean prime ideal theorem does not imply the axiom of choice.
He also introduced the notions of Lévy hierarchy of the formulas of set theory, Levy collapse and the Feferman–Levy model.
His students include Dov Gabbay, Moti Gitik, and Menachem Magidor.
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