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The Type $ω$-Vaught's Conjecture for $ω$-stable Theories
We propose a new variant of Vaught's conjecture, based on Martin's (model-theoretic) conjecture and the $ω$-Vaught's conjecture of Gonzalez and Montalbán. For $ω$-stable theories, we prove the conjecture by analyzing in detail Bouscaren's and Shelah-Harrington-Makkai's proofs of Martin's conjecture
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