A generalization of the concept of |omega-consistency

Journal of Symbolic Logic 19 (3):183 - 196 (1954)
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DOI 10.2307/2268617
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Compact Extensions of L(Q).M. Magidor & J. I. Malitz - 1977 - Annals of Mathematical Logic 11 (2):217--261.
Barwise: Infinitary Logic and Admissible Sets.H. Jerome Keisler & Julia F. Knight - 2004 - Bulletin of Symbolic Logic 10 (1):4-36.
Completeness Theorems for Topological Models.Joseph Sgro - 1977 - Annals of Mathematical Logic 11 (2):173-193.

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