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Preprint Number 1348
1348. Marcos Mazari Armida and Sebastien Vasey Universal classes near ℵ_1 E-mail: Submission date: 7 December 2017 Abstract: Shelah has provided sufficient conditions for an L_{ω_1,
ω}-sentence ψ to have arbitrarily large models and for a
Morley-like
theorem to hold of ψ. These conditions involve structural and
set-theoretic assumptions on all the ℵ_n's. Using tools of Boney,
Shelah, and the second author, we give assumptions on ℵ_0 and
ℵ_1
which suffice when ψ is restricted to be universal: Mathematics Subject Classification: Primary 03C48. Secondary: 03C45, 03C52, 03C55, 03C75 Keywords and phrases: |

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