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Scattered sentences have few separable randomizations. (English) Zbl 1481.03013

Summary: In the paper [in: Beyond first order model theory. Boca Raton, FL: CRC Press. 189–220 (2017; Zbl 1433.03097)], H. J. 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.

MSC:

03C15 Model theory of denumerable and separable structures
03C65 Models of other mathematical theories
03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

Citations:

Zbl 1433.03097
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References:

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