Abstract
In the paper Randomizations of Scattered Sentences, Keisler showed that if Martin’s axiom for aleph one holds, then every scattered sentence has few separable randomizations, and asked whether the conclusion could be proved in ZFC alone. We show here that the answer is “yes”. It follows that the absolute Vaught conjecture holds if and only if every \(L_{\omega _1\omega }\)-sentence with few separable randomizations has countably many countable models.
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The work of Andrews was partially supported by NSF Grant DMS-1600228. The work of Goldbring was partially supported by NSF CAREER Grant DMS-1349399. Hachtman was partially supported by NSF Grant DMS-1246844.
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Andrews, U., Goldbring, I., Hachtman, S. et al. Scattered sentences have few separable randomizations. Arch. Math. Logic 59, 743–754 (2020). https://doi.org/10.1007/s00153-020-00718-7
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DOI: https://doi.org/10.1007/s00153-020-00718-7