Abstract
The logicL(I) is introduced. Compactness and Löwenheim-Skolem theorems for topological models are proved. Several axiomatizations are given and proved to be complete. Interpolation- and preservation theorems are proved using consistency properties. A Back and Forth criterion for elementary equivalence is proved. Most of the results are extended (appropriately) to infinitary logic.
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Makowsky, J.A., Ziegler, M. Topological model theory with an interior operator: Consistency properties and back — and forth arguments. Arch math Logik 21, 37–54 (1981). https://doi.org/10.1007/BF02011632
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DOI: https://doi.org/10.1007/BF02011632