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1	Abstract Logics and Lindström's Theorem / Abstrakta Logiker och Lindströms Sats Bengtsson, Niclas January 2023 (has links) A definition of abstract logic is presented. This is used to explore and compare some abstract logics, such as logics with generalised quantifiers and infinitary logics, and their properties. Special focus is given to the properties of completeness, compactness, and the Löwenheim-Skolem property. A method of comparing different logics is presented and the concept of equivalent logics introduced. Lastly a proof is given for Lindström's theorem, which provides a characterization of elementary logic, also known as first-order logic, as the strongest logic for which both the compactness property and the Löwenheim-Skolem property, holds. model theory abstract model theory logic mathematical logic abstract logic Lindström's Theorem infinitary logics strength of logics cardinality quantifiers modellteori abstrakt modellteori logik matematisk logik abstrakt logik Lindströms sats Algebra and Logic Algebra och logik Philosophy Filosofi