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Answer by Asaf Karagila for Cardinal arithmetic under determinacy
Starting from $L(\Bbb R)$, we can take a symmetric extension which preserves $\sf DC$ and adds an $\omega_1$-amorphous set, just somewhere far above $\Theta$.So we cannot prove that (1) or (2) hold for...
View ArticleCardinal arithmetic under determinacy
Work in a reasonable theory of determinacy such as $\mathsf{ZF+DC+AD}$. Which of the following identities are true for arbitrary infinite sets?$|A^2|=|A^3|$ (motivated by an MSE question that asks if...
View ArticleAnswer by user534667 for Cardinal arithmetic under determinacy
Simon Thomas "Superrigidity and countable Borel equivalence relations" Corollary 4.9 gives a countable Borel equivalence relation E shows E and 2E are not Borel bireducible. (The examples involve...
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