Author

R. Knight

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Preprint Oct 2026

A counterexample to Vaught's Conjecture for $L_{\omega_1,\omega}$

We construct a sentence of $L_{\omega_1,\omega}$ having exactly $\aleph_1$ 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...

N. Ackerman, Cameron E. Freer, R. Knight · 0 citations