A generalization of the concept of ω-consistency

Journal of Symbolic Logic 19 (3):183-196 (1954)
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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.
Compact extensions of L(Q).Menachem Magidor & Jerome Malitz - 1977 - Annals of Mathematical Logic 11 (2):217--261.

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