Newelski, Ludomir A proof of Saffe’s conjecture. (English) Zbl 0716.03024 Fundam. Math. 134, No. 2, 143-155 (1990). Summary: We prove that if T is weakly minimal, \(p_ 0\in S(\emptyset)\) is non- isolated and has infinite multiplicity, then T has \(2^{\aleph_ 0}\) countable models, thus proving Saffe’s conjecture. Together with S. Buechler’s results [Lect. Notes Math. 1292, 32-71 (1987; Zbl 0655.03022); J. Symb. Logic 53, No.2, 625-635 (1988; Zbl 0665.03020)], this completes the proof of Vaught’s conjecture for weakly minimal theories. Cited in 1 ReviewCited in 7 Documents MSC: 03C15 Model theory of denumerable and separable structures 03C45 Classification theory, stability, and related concepts in model theory Keywords:countable models; Saffe’s conjecture; Vaught’s conjecture; weakly minimal theories Citations:Zbl 0655.03022; Zbl 0665.03020 PDFBibTeX XMLCite \textit{L. Newelski}, Fundam. Math. 134, No. 2, 143--155 (1990; Zbl 0716.03024) Full Text: DOI EuDML