A proof of Vaught's conjecture for \(\omega\)-stable theories
The famous Vaught's conjecture is the statement that for any countable theory T in \(L_{\omega_ 1\omega}\) the number of isomorphism types of countable models of T is either \(2^{\aleph_ 0}\) or at most \(\aleph_ 0\). The question is still open even for theories in finitary logic. In the paper under review Vaught's conjecture is proved for T a first-order countable complete \(\omega\)-stable theory. The results of the paper are due to Shelah.
scientific article; zbMATH DE number 3935015
scientific article