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The second-order version of Morley’s theorem on the number of countable models does not require large cardinals

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Abstract

The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large cardinals. We here dispense with them.

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Acknowledgements

We thank the referee for their comments, suggestions and corrections that greatly improve the quality of this paper.

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  1. Department of Mathematics, University of Toronto, 40 St. George St., Toronto, ON, M5S 2E4, Canada

    Franklin D. Tall & Jing Zhang

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  1. Franklin D. Tall
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  2. Jing Zhang
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Correspondence to Franklin D. Tall.

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Tall, F.D., Zhang, J. The second-order version of Morley’s theorem on the number of countable models does not require large cardinals. Arch. Math. Logic 63, 483–490 (2024). https://doi.org/10.1007/s00153-024-00907-8

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  • DOI: https://doi.org/10.1007/s00153-024-00907-8

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