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  1. Iterated extended ultrapowers and supercompactness without choice.Mitchell Spector - 1991 - Annals of Pure and Applied Logic 54 (2):179-194.
    Working in ZF + DC with no additional use of the axiom of choice, we show how to iterate the extended ultrapower construction of Spector . This generalizes the technique of iterated ultrapowers to choiceless set theory. As an application, we prove the following theorem: Assume V = LU[κ] + “κ is λ-supercompact with normal ultrafilter U” + DC. Then for every sufficiently large regular cardinal ρ, there exists a set-generic extension V[G] of the universe in which there exists for (...)
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  • On a Spector Ultrapower for the Solovay Model.Vladimir Kanovei & Michiel van Lambalgen - 1997 - Mathematical Logic Quarterly 43 (3):389-395.
    We prove that a Spector‐like ultrapower extension ???? of a countable Solovay model ???? (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension ????[a], where a is a random real over ????. The proof involves the Solovay almost everywhere uniformization technique.
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