Abstract
It is proved that the existence of supercompact cardinal is equivalent to a certain Skolem-Löwenheim Theorem for second order logic, whereas the existence of extendible cardinal is equivalent to a certain compactness theorem for that logic. It is also proved that a certain axiom schema related to model theory implies the existence of many extendible cardinals.
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References
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This paper is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor Azriel Levy, for whose help and encouragement the author is greatly indebted.
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Magidor, M. On the role of supercompact and extendible cardinals in logic. Israel J. Math. 10, 147–157 (1971). https://doi.org/10.1007/BF02771565
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DOI: https://doi.org/10.1007/BF02771565