5 Counterexamples to Vaught ’ s Conjecture
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چکیده
A sentence σ ∈ L ω1,ω is a counterexample to Vaught's Conjecture, or simply a counterexample, if ℵ 0 < I(σ, ℵ 0) < 2 ℵ0 , i.e., σ has uncountably many countable models but fewer than continuum many models. Fix σ a counterexample. A key fact about counterexamples is that there are few types for any count-able fragment. Let F be a fragment. Let
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