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A proof of Saffe’s conjecture. (English) Zbl 0716.03024

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.

MSC:

03C15 Model theory of denumerable and separable structures
03C45 Classification theory, stability, and related concepts in model theory
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