The Hanf number of second order logic

Journal of Symbolic Logic 37 (3):588-594 (1972)
Abstract
We prove, among other things, that the number mentioned above cannot be shown to exist without using some $\Pi_1(\mathscr{P})$ instance of the axiom of replacement
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DOI 10.2307/2272748
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Barwise: Infinitary Logic and Admissible Sets.H. Jerome Keisler & Julia F. Knight - 2004 - Bulletin of Symbolic Logic 10 (1):4-36.

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