Work

A counterexample to Vaught's Conjecture for $L_{ω_1,ω}$

Year: 2026

Type: preprint

Abstract: We construct a sentence of $L_{ω_1,ω}$ 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 in Lean.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15217

Authors: Ackerman, Nathanael L., Freer, Cameron E., Knight, Robin W.

Institutions: Harvard University, University of Oxford, Massachusetts Institute of Technology

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221766611

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