A note on counterexamples to the Vaught conjecture
In this short note the following consequence of a previous theorem by the author [J. Math. Log. 2, 113--144 (2002; Zbl 1010.03036)] is proved: if Vaught's conjecture for \(\mathcal{L}_{\omega_1 \omega}\) is false then there is a counterexample with no models of cardinality larger than \(\aleph_1\). The proof uses tools from descriptive set theory and in particular from the study of Polish groups actions.
scientific article; zbMATH DE number 5178765