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Categoricity in ℵ1 of sentences in\(L_{\omega _1 ,\omega } (Q)\)

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Abstract

We investigate the categoricity and number of non-isomorphic models in ℵ1 of sentences in\(L_{\omega _1 ,\omega } (Q)\). AssumingV=L we prove that no sentence in\(L_{\omega _1 ,\omega } (Q)\) has exactly one uncountable model. Thus partially answering problem 24 of a problem list by Friedman.

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  1. Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah

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  1. Saharon Shelah
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Shelah, S. Categoricity in ℵ1 of sentences in\(L_{\omega _1 ,\omega } (Q)\) . Israel J. Math. 20, 127–148 (1975). https://doi.org/10.1007/BF02757882

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