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تسجيل مستخدم جديدAn undecidable extension of Morleys theorem on the number of countable models
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We show that Morleys theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of $sigma$-projective equivalence relations in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.
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