1 - 10 of 15 articles
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...
We generalize Keisler's omitting types theorem forL(Q) in the ℵ1-interpretation, to most cases in which Chang's two cardinal theorem applies. As an application we answer positively a question of Magidor and Malitz on the compactness of their logic in cardinalities higher than ℵ1.
Various compact logics such as stationary logic, positive logic, logics with various cardinality quantifiers and cofinality quantifiers are studied. Counterexamples to the theorems of Beth and Craig are given. Back and forth arguments are studied for the first two logics, transfer theorems...
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