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Generalized quantifiers and compact logic


Author: Saharon Shelah
Journal: Trans. Amer. Math. Soc. 204 (1975), 342-364
MSC: Primary 02H05; Secondary 02B20
DOI: https://doi.org/10.1090/S0002-9947-1975-0376334-6
MathSciNet review: 0376334
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Abstract: We solve a problem of Friedman by showing the existence of a logic stronger than first-order logic even for countable models, but still satisfying the general compactness theorem, assuming e.g. the existence of a weakly compact cardinal. We also discuss several kinds of generalized quantifiers.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0376334-6
Article copyright: © Copyright 1975 American Mathematical Society

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