Vopěnka's principle and compact logics

Journal of Symbolic Logic 50 (1):42-48 (1985)
We study the effects of Vopěnka's principle on properties of model theoretic logics. We show that Vopěnka's principle is equivalent to the assumption that every finitely generated logic has a compact cardinal. We show also that it is equivalent to the assumption that every such logic has a global Hanf number
Keywords Large Cardinals   abstract model theory
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DOI 10.2307/2273786
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