There are reasonably nice logics

Journal of Symbolic Logic 56 (1):300-322 (1991)
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Wilfrid Hodges
British Academy

Citations of this work

Recursive logic frames.Saharon Shelah & Jouko Väänänen - 2006 - Mathematical Logic Quarterly 52 (2):151-164.

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References found in this work

Remarks in abstract model theory.Saharon Shelah - 1985 - Annals of Pure and Applied Logic 29 (3):255-288.
Infinite games and reduced products.W. Hodges - 1981 - Annals of Mathematical Logic 20 (1):77.
Compact extensions of L(Q).Menachem Magidor & Jerome Malitz - 1977 - Annals of Mathematical Logic 11 (2):217--261.

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