A counterexample to Vaught's Conjecture for Lω1,ω
Nathanael L. Ackerman, Cameron E. Freer, Robin W. Knight
Abstract
We construct a sentence of Lω1,ω having exactly 1 many countable models up to isomorphism, but no perfect set of non-isomorphic models. This disproves Vaught's conjecture for infinitary logic. The construction follows a framework devised by Robin Knight, and the proof has been formally verified in Lean.
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